Outline of logic

Logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

formal science Formal science is a branch of science studying disciplines concerned with abstract structures described by formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game t ...

reason Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, ...

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...

formal system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...

fallacies A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument which may appear stronger than it really is if the fallacy is not spotted. The term in the Western intellectual tradition was intr ...

paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...

fallacious A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument which may appear stronger than it really is if the fallacy is not spotted. The term in the Western intellectual tradition was intr ...

arguments An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectic ...

Philosophy of logic Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application ...

A priori and a posteriori ("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current ...

Description Description is the pattern of narrative development that aims to make vivid a place, object, character, or group. Description is one of four rhetorical modes (also known as ''modes of discourse''), along with exposition, argumentation, and narra ...

Entailment Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...

Logical form In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguou ...

Logical implication Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...

Logical truth Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement whic ...

Necessity Necessary or necessity may refer to: * Need ** An action somebody may feel they must do ** An important task or essential thing to do at a particular time or by a particular moment * Necessary and sufficient condition, in logic, something that i ...

Material conditional The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q i ...

Meaning (linguistic) Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...

Paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

list A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby unio ...

Possible world A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their me ...

Probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...

Reason Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, ...

Reference Reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another object. The first object in this relation is said to ''refer to'' the second object. It is called a '' name'' ...

Semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comp ...

Strict conditional In logic, a strict conditional (symbol: \Box, or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necess ...

Truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as belie ...

Truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Computing In some pro ...

Affine logic Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linear logic with weakening. The name "affine logic" is associated with linear logic, to which it differs by all ...

Alethic logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

Buddhist logic Buddhist logico-epistemology is a term used in Western scholarship for ''pramāṇa-vāda'' (doctrine of proof) and ''Hetu-vidya'' (science of causes). Pramāṇa-vāda is an epistemological study of the nature of knowledge; Hetu-vidya is a syste ...

Categorical logic __NOTOC__ Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. In broad terms, categ ...

Deontic logic Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It ...

Dependence logic Dependence logic is a logical formalism, created by Jouko Väänänen, which adds ''dependence atoms'' to the language of first-order logic. A dependence atom is an expression of the form =\!\!(t_1 \ldots t_n), where t_1 \ldots t_n are terms, and c ...

Deviant logic Deviant logic is a type of logic incompatible with classical logic. Philosopher Susan Haack uses the term ''deviant logic'' to describe certain non-classical systems of logic. In these logics: * the set of well-formed formulas generated equals th ...

Doxastic logic Doxastic logic is a type of logic concerned with reasoning about beliefs. The term ' derives from the Ancient Greek (''doxa'', "opinion, belief"), from which the English term '' doxa'' ("popular opinion or belief") is also borrowed. Typically, a ...

Epistemic logic Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applica ...

First-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

Formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...

Higher-order logic mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more express ...

Infinitary logic An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In particular, infinitary logics may fail to be co ...

Intensional logic Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe (''extensions''), by additional quantifiers that range over terms that may have such individuals ...

Intermediate logic In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent superintuitionistic logic; thus, consistent superintuitionistic logics are called intermediate l ...

Intuitionistic logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems ...

Many-valued logic Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false ...

Mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

Metalogic Metalogic is the study of the metatheory of logic. Whereas ''logic'' studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems.Harry GenslerIntroduction to Logic Routledge, ...

Minimal logic Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson. It is an intuitionistic and paraconsistent logic, that rejects both the law of the excluded middle as well as the principle of explosion ...

Non-classical logic Non-classical logics (and sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done, including by way of ...

Non-monotonic logic A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reasoning), i.e., a kind of inference in which re ...

Predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

Propositional logic Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations b ...

Provability logic Provability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as Peano arithmetic. Examples ...

Quantum logic In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The field takes as its starting point an observ ...

Relevance logic Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but ...

Sequential logic In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past inputs, the input history. This is in contrast to ''combinational logic'', whose output i ...

Substructural logic In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening, contraction, exchange or associativity. Two of the more significant substructural logics are r ...

Temporal logic In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I ...

Term logic In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...

Traditional logic In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...

Argumentation theory Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic, dialectic, and rhetoric, argumentation theory, incl ...

Argument map An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes the key components of the argument, traditionally called the '' conclusion'' and the ''premises'', also called ''con ...

Analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

Belief A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take ...

Belief bias Belief bias is the tendency to judge the strength of arguments based on the plausibility of their conclusion rather than how strongly they support that conclusion. A person is more likely to accept an argument that supports a conclusion that alig ...

Bias Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group ...

Critical pedagogy Critical pedagogy is a philosophy of education and social movement that developed and applied concepts from critical theory and related traditions to the field of education and the study of culture. It insists that issues of social justice and de ...

Critical reading Critical reading is a form of language analysis that does not take the given text at face value, but involves a deeper examination of the claims put forth as well as the supporting points and possible counterarguments. The ability to reinterpret ...

Emotional reasoning Emotional reasoning is a cognitive process by which an individual concludes that their emotional reaction proves something is true, despite contrary empirical evidence. Emotional reasoning creates an 'emotional truth', which may be in direct c ...

Explanation An explanation is a set of statements usually constructed to describe a set of facts which clarifies the causes, context, and consequences of those facts. It may establish rules or laws, and may clarify the existing rules or laws in relatio ...

Explanatory power Explanatory power is the ability of a hypothesis or theory to explain the subject matter effectively to which it pertains. Its opposite is ''explanatory impotence''. In the past, various criteria or measures for explanatory power have been prop ...

Higher-order thinking Higher-order thinking, known as higher order thinking skills (HOTS), is a concept of education reform based on learning taxonomies (such as Bloom's taxonomy). The idea is that some types of learning require more cognitive processing than others, ...

Propaganda techniques A number of propaganda techniques based on social psychology, social psychological research are used to generate propaganda. Many of these same techniques can be classified as Informal fallacy, logical fallacies, since propagandists use arguments ...

Pseudophilosophy Pseudophilosophy is a term applied to a philosophical idea or system which does not meet an expected set of philosophical standards. There is no universally accepted set of standards, but there are similarities and some common ground. Definitions ...

Relevance Relevance is the concept of one topic being connected to another topic in a way that makes it useful to consider the second topic when considering the first. The concept of relevance is studied in many different fields, including cognitive sci ...

Rigour Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as ma ...

Socratic questioning Socratic questioning (or Socratic maieutics) was named after Socrates. He used an educational method that focused on discovering answers by asking questions from his students. According to Plato, who was one of his students, Socrates believed t ...

Theory of justification Justification (also called epistemic justification) is the property of belief that qualifies it as knowledge rather than mere opinion. Epistemology is the study of reasons that someone holds a rationally admissible belief (although the term is a ...

Vagueness In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is ...

Anti-psychologism In logic, anti-psychologism (also logical objectivism or logical realism) is a theory about the nature of logical truth, that it does not depend upon the contents of human ideas but exists independent of human ideas. Overview The anti-psychologisti ...

Conceptualism In metaphysics, conceptualism is a theory that explains universality of particulars as conceptualized frameworks situated within the thinking mind. Intermediate between nominalism and realism, the conceptualist view approaches the metaphysical co ...

Constructivism Constructivism may refer to: Art and architecture * Constructivism (art), an early 20th-century artistic movement that extols art as a practice for social purposes * Constructivist architecture, an architectural movement in Russia in the 1920s a ...

Conventionalism Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality. Unspoken rules play a key role in the philosophy's structur ...

Counterpart theory In philosophy, specifically in the area of metaphysics, counterpart theory is an alternative to standard ( Kripkean) possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but diffe ...

Deflationary theory of truth In philosophy and logic, a deflationary theory of truth (also semantic deflationism or simply deflationism) is one of a family of theories that all have in common the claim that assertions of predicate truth of a statement do not attribute a prop ...

Dialetheism Dialetheism (from Greek 'twice' and 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true ...

Fictionalism Fictionalism is the view in philosophy according to which statements that appear to be descriptions of the world should not be construed as such, but should instead be understood as cases of "make believe", of pretending to treat something as liter ...

Formalism (philosophy) The term ''formalism'' describes an emphasis on form over content or meaning in the arts, literature, or philosophy. A practitioner of formalism is called a ''formalist''. A formalist, with respect to some discipline, holds that there is no transc ...

Illuminationist philosophy Illuminationism (Persian حكمت اشراق ''hekmat-e eshrāq'', Arabic: حكمة الإشراق ''ḥikmat al-ishrāq'', both meaning "Wisdom of the Rising Light"), also known as ''Ishrāqiyyun'' or simply ''Ishrāqi'' (Persian اشراق, Arab ...

Logical atomism Logical atomism is a philosophical view that originated in the early 20th century with the development of analytic philosophy. Its principal exponent was the British philosopher Bertrand Russell. It is also widely held that the early works of his ...

Logicism In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all ...

Nominalism In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are at least two main versions of nominalism. One version denies the existence of universalsthings ...

Pragmatism Pragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. ...

Preintuitionism In the philosophy of mathematics, the pre-intuitionists were a small but influential group who informally shared similar philosophies on the nature of mathematics. The term itself was used by L. E. J. Brouwer, who in his 1951 lectures at Cambridge ...

Psychologism Psychologism is a family of philosophical positions, according to which certain psychological facts, laws, or entities play a central role in grounding or explaining certain non-psychological facts, laws, or entities. The word was coined by Johan ...

Ramism Ramism was a collection of theories on rhetoric, logic, and pedagogy based on the teachings of Petrus Ramus, a French academic, philosopher, and Huguenot convert, who was murdered during the St. Bartholomew's Day massacre in August 1572. Accord ...

Semantic theory of truth A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences. Origin The semantic conception of truth, which is related in different ways to both the correspondence and deflati ...

Sophism A sophist ( el, σοφιστής, sophistes) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics, and mathematics. They taught ' ...

Trivialism Trivialism is the logical theory that all statements (also known as propositions) are true and that all contradictions of the form "p and not p" (e.g. the ball is red and not red) are true. In accordance with this, a trivialist is a person who b ...

Ultrafinitism In the philosophy of mathematics, ultrafinitism (also known as ultraintuitionism,International Workshop on Logic and Computational Complexity, ''Logic and Computational Complexity'', Springer, 1995, p. 31. strict formalism,St. Iwan (2000),On the U ...

list A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby unio ...

Formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...

formal language In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of sy ...

Propositional variable In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of proposit ...

Predicate variable In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning). Common symbols for denoting predi ...

Metavariable In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. For instance, in the sentence :''Let A and B be two sente ...

Logical constant In logic, a logical constant of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal. Two important types of logical constants are logical connectives and quantifiers. The equality predicate (us ...

Logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...

Brackets A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. Typically deployed in symmetric pairs, an individual bracket may be identified as a 'left' or ' ...

Logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...

Converse implication In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication ''P'' → ''Q'', the converse is ''Q'' → ''P''. For the categorical proposi ...

Converse nonimplication In logic, converse nonimplication is a logical connective which is the negation of converse implication (equivalently, the negation of the converse of implication). Definition Converse nonimplication is notated P \nleftarrow Q, or P \not \subs ...

Exclusive or Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...

Logical biconditional In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective (\leftrightarrow) used to conjoin two statements and to form the statement " if and only if ", where is known as th ...

Logical conjunction In logic, mathematics and linguistics, And (\wedge) is the truth-functional operator of logical conjunction; the ''and'' of a set of operands is true if and only if ''all'' of its operands are true. The logical connective that represents thi ...

Logical disjunction In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor ...

Sheffer stroke In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called nand ("not and") ...

Atomic formula In mathematical logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformu ...

Open sentence An open formula is a formula that contains at least one free variable. An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like ''true'' or ...

Proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

Analytic proposition Generally speaking, analytic (from el, ἀναλυτικός, ''analytikos'') refers to the "having the ability to analyze" or "division into elements or principles". Analytic or analytical can also have the following meanings: Chemistry * A ...

Atomic sentence In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences ...

Clause (logic) In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives. A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, ...

Contradiction In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's ...

Logical truth Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement whic ...

Propositional formula In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional for ...

Sentence (mathematical logic) :''This article is a technical mathematical article in the area of predicate logic. For the ordinary English language meaning see Sentence (linguistics), for a less technical introductory article see Statement (logic).'' In mathematical logic, a ...

Sequent In mathematical logic, a sequent is a very general kind of conditional assertion. : A_1,\,\dots,A_m \,\vdash\, B_1,\,\dots,B_n. A sequent may have any number ''m'' of condition formulas ''Ai'' (called " antecedents") and any number ''n'' of ass ...

Theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of t ...

list A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby unio ...

Biconditional elimination Biconditional elimination is the name of two valid rules of inference of propositional logic. It allows for one to infer a conditional from a biconditional. If P \leftrightarrow Q is true, then one may infer that P \to Q is true, and also th ...

Biconditional introduction In propositional calculus, propositional logic, biconditional introductionCopi and Cohen is a Validity (logic), valid rule of inference. It allows for one to inference, infer a Logical biconditional, biconditional from two Material conditional, ...

Conjunction introduction Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. I ...

Constructive dilemma Constructive dilemmaCopi and Cohen is a valid rule of inference of propositional logic. It is the inference that, if ''P'' implies ''Q'' and ''R'' implies ''S'' and either ''P'' or ''R'' is true, then either ''Q or S'' has to be true. In sum, ...

Contraposition (traditional logic) In traditional logic, contraposition is a form of immediate inference in which a proposition is inferred from another and where the former has for its subject the contradictory of the original logical proposition's predicate. In some cases, contr ...

Conversion (logic) In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication ''P'' → ''Q'', the converse is ''Q'' → ''P''. For the categorical propositi ...

De Morgan's laws In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British math ...

Destructive dilemma Destructive dilemmaMoore and Parker is the name of a valid rule of inference of propositional logic. It is the inference that, if ''P'' implies ''Q'' and ''R'' implies ''S'' and either ''Q'' is false or ''S'' is false, then either ''P'' or '' ...

Disjunction elimination In propositional logic, disjunction elimination (sometimes named proof by cases, case analysis, or or elimination), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It ...

Disjunction introduction Disjunction introduction or addition (also called or introduction) is a rule of inference of propositional logic and almost every other deduction system. The rule makes it possible to introduce disjunctions to logical proofs. It is the infer ...

Disjunctive syllogism In classical logic, disjunctive syllogism (historically known as ''modus tollendo ponens'' (MTP), Latin for "mode that affirms by denying") is a valid argument form which is a syllogism having a disjunctive statement for one of its premise ...

Double negation elimination In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition ''A'' is logically equivalent to ''not (not ...

Generalization (logic) In predicate logic, generalization (also universal generalization or universal introduction,Moore and Parker GEN) is a valid inference rule. It states that if \vdash \!P(x) has been derived, then \vdash \!\forall x \, P(x) can be derived. Gener ...

Hypothetical syllogism In classical logic, a hypothetical syllogism is a valid argument form, a syllogism with a conditional statement for one or both of its premises. An example in English: :If I do not wake up, then I cannot go to work. :If I cannot go to work, then ...

Law of excluded middle In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradi ...

Law of identity In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are bui ...

Modus tollens In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens' ...

Obversion In traditional logic, obversion is a "type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, ...

Principle of contradiction In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the sa ...

Resolution (logic) In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically ...

Transposition (logic) In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated. It is the inference from the t ...

Formal proof In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the seq ...

List of first-order theories In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model theory and some of their properties. Preliminaries For every natural mathematical structure ...

Metalinguistic variable In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. For instance, in the sentence :''Let A and B be two sente ...

Deductive system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A for ...

Metatheorem In logic, a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metathe ...

Metatheory A metatheory or meta-theory is a theory whose subject matter is theory itself, aiming to describe existing theory in a systematic way. In mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. ...

Propositional logic Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations b ...

Absorption law In algebra, the absorption law or absorption identity is an identity linking a pair of binary operations. Two binary operations, ¤ and ⁂, are said to be connected by the absorption law if: :''a'' ¤ (''a'' ⁂ ''b'') = ''a'' ⁂ (''a'' ¤ ''b ...

Clause (logic) In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives. A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, ...

Distributive property In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the equality x \cdot (y + z) = x \cdot y + x \cdot z is always true in elementary algebra. For example, in elementary arithmet ...

Entailment Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...

Formation rule In mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language. These rules only address the location and manipulation of the st ...

Functional completeness In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression.. ("Complete set of logical connectives").. ( ...

Intermediate logic In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent superintuitionistic logic; thus, consistent superintuitionistic logics are called intermediate l ...

Literal (mathematical logic) In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. L ...

Logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...

Negation normal form In mathematical logic, a formula is in negation normal form (NNF) if the negation operator (\lnot, ) is only applied to variables and the only other allowed Boolean operators are conjunction (\land, ) and disjunction (\lor, ). Negation normal for ...

Open sentence An open formula is a formula that contains at least one free variable. An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like ''true'' or ...

Propositional calculus Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations ...

Propositional formula In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional for ...

Propositional variable In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of proposit ...

Strict conditional In logic, a strict conditional (symbol: \Box, or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necess ...

Substitution instance Substitution is a fundamental concept in logic. A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols by other expressions. ...

Truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional argumen ...

Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...

list A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby unio ...

Complete Boolean algebra In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct Boolean-valued models of set theory in the theory of forcing. Every Boolea ...

Monadic Boolean algebra In abstract algebra, a monadic Boolean algebra is an algebraic structure ''A'' with signature :⟨·, +, ', 0, 1, ∃⟩ of type ⟨2,2,1,0,0,1⟩, where ⟨''A'', ·, +, ', 0, 1⟩ is a Boolean algebra. The monadic/unary ...

Two-element Boolean algebra In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose ''underlying set'' (or universe or ''carrier'') ''B'' is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that ''B ...

Absorption law In algebra, the absorption law or absorption identity is an identity linking a pair of binary operations. Two binary operations, ¤ and ⁂, are said to be connected by the absorption law if: :''a'' ¤ (''a'' ⁂ ''b'') = ''a'' ⁂ (''a'' ¤ ''b ...

Laws of Form ''Laws of Form'' (hereinafter ''LoF'') is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. ''LoF'' describes three distinct logical systems: * The "primary arithmetic" (described in C ...

De Morgan's laws In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British math ...

Boolean domain In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include ''false'' and ''true''. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as ...

Boolean expression In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean c ...

Boolean ring In mathematics, a Boolean ring ''R'' is a ring for which ''x''2 = ''x'' for all ''x'' in ''R'', that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean al ...

Boolean function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...

Boolean-valued function A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = ), whose elements are i ...

Parity function In Boolean algebra, a parity function is a Boolean function whose value is one if and only if the input vector has an odd number of ones. The parity function of two inputs is also known as the XOR function. The parity function is notable for its r ...

Conditioned disjunction In logic, conditioned disjunction (sometimes called conditional disjunction) is a ternary logical connective introduced by Church. Given operands ''p'', ''q'', and ''r'', which represent truth-valued propositions, the meaning of the conditioned d ...

Field of sets In mathematics, a field of sets is a mathematical structure consisting of a pair ( X, \mathcal ) consisting of a set X and a family \mathcal of subsets of X called an algebra over X that contains the empty set as an element, and is closed un ...

Functional completeness In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression.. ("Complete set of logical connectives").. ( ...

Logic redundancy Logic redundancy occurs in a digital gate network containing circuitry that does not affect the static logic function. There are several reasons why logic redundancy may exist. One reason is that it may have been added deliberately to suppress tra ...

Logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...

Logical matrix A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1) matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. Matrix representation ...

Product term In Boolean logic, a product term is a conjunction of literals, where each literal is either a variable or its negation. Examples Examples of product terms include: :A \wedge B :A \wedge (\neg B) \wedge (\neg C) :\neg A Origin The terminology come ...

True quantified Boolean formula In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas. A (fully) quantified Boolean formula is a formula in quantified propositional logic where every variable is quantified ( ...

Truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional argumen ...

Predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

Atomic formula In mathematical logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformu ...

Atomic sentence In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences ...

First-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

First-order predicate In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s).. Compare second-order predicate and higher-order predicate. This is not to be confused with a one-place predicate o ...

Formation rule In mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language. These rules only address the location and manipulation of the st ...

Free variables and bound variables In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not ...

Generalization (logic) In predicate logic, generalization (also universal generalization or universal introduction,Moore and Parker GEN) is a valid inference rule. It states that if \vdash \!P(x) has been derived, then \vdash \!\forall x \, P(x) can be derived. Gener ...

Monadic predicate calculus In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbo ...

Predicate (mathematical logic) In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P(a), the symbol P is a predicate which applies to the individual constant a. Similarly, in the formula R(a,b), R is a predicat ...

Predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

Predicate variable In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning). Common symbols for denoting predi ...

Sentence (mathematical logic) :''This article is a technical mathematical article in the area of predicate logic. For the ordinary English language meaning see Sentence (linguistics), for a less technical introductory article see Statement (logic).'' In mathematical logic, a ...

Universal instantiation In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with '' dictum de omni'') is a valid rule of inference from a truth about each member of a class of individuals ...

Finitary relation In mathematics, a finitary relation over sets is a subset of the Cartesian product ; that is, it is a set of ''n''-tuples consisting of elements ''x'i'' in ''X'i''. Typically, the relation describes a possible connection between the elemen ...

Antisymmetric relation In mathematics, a binary relation R on a set X is antisymmetric if there is no pair of ''distinct'' elements of X each of which is related by R to the other. More formally, R is antisymmetric precisely if for all a, b \in X, \text \,aRb\, \t ...

Asymmetric relation In mathematics, an asymmetric relation is a binary relation R on a set X where for all a, b \in X, if a is related to b then b is ''not'' related to a. Formal definition A binary relation on X is any subset R of X \times X. Given a, b \in X, ...

Bijection, injection and surjection In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which '' arguments'' (input expressions from the domain) and '' images'' (output expressions from the codomain) are related or ''m ...

Connected relation In mathematics, a relation on a set is called connected or total if it relates (or "compares") all pairs of elements of the set in one direction or the other while it is called strongly connected if it relates pairs of elements. As described ...

Converse relation In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent&n ...

Coreflexive relation In mathematics, a binary relation ''R'' on a set ''X'' is reflexive if it relates every element of ''X'' to itself. An example of a reflexive relation is the relation " is equal to" on the set of real numbers, since every real number is equal to ...

Covering relation In mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are immediate neighbours. The covering relation is commonly used to graphically expres ...

Cyclic order In mathematics, a cyclic order is a way to arrange a set of objects in a circle. Unlike most structures in order theory, a cyclic order is not modeled as a binary relation, such as "". One does not say that east is "more clockwise" than west. Ins ...

Dependence relation In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence. Let X be a set (mathematics), set. A (binary) relation \triangleleft between an element a of X and a subset S of X is called a ''depend ...

Dependency relation In computer science, in particular in concurrency (computer science), concurrency theory, a dependency relation is a binary relation on a finite domain \Sigma, symmetric relation, symmetric, and reflexive relation, reflexive; i.e. a finite toleran ...

Directed set In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation \,\leq\, (that is, a preorder), with the additional property that every pair of elements ha ...

Euclidean relation In mathematics, Euclidean relations are a class of binary relations that formalize " Axiom 1" in Euclid's ''Elements'': "Magnitudes which are equal to the same are equal to each other." Definition A binary relation ''R'' on a set ''X'' is Euclide ...

Homogeneous relation In mathematics, a homogeneous relation (also called endorelation) over a set ''X'' is a binary relation over ''X'' and itself, i.e. it is a subset of the Cartesian product . This is commonly phrased as "a relation on ''X''" or "a (binary) relation ...

Idempotence Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of pl ...

Intransitivity In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. This may include any relation that is not transitive, or the stronger property of antitransitivity, which descri ...

Partial function In mathematics, a partial function from a set to a set is a function from a subset of (possibly itself) to . The subset , that is, the domain of viewed as a function, is called the domain of definition of . If equals , that is, if is de ...

Partially ordered set In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a bina ...

Propositional function In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (''x'') that is not defined or specified (thus be ...

Quasitransitive relation The mathematical notion of quasitransitivity is a weakened version of transitivity that is used in social choice theory and microeconomics. Informally, a relation is quasitransitive if it is symmetric for some values and transitive elsewhere. Th ...

Reflexive relation In mathematics, a binary relation ''R'' on a set ''X'' is reflexive if it relates every element of ''X'' to itself. An example of a reflexive relation is the relation " is equal to" on the set of real numbers, since every real number is equal ...

Serial relation In set theory a serial relation is a homogeneous relation expressing the connection of an element of a sequence to the following element. The successor function used by Peano to define natural numbers is the prototype for a serial relation. Bertran ...

Surjective function In mathematics, a surjective function (also known as surjection, or onto function) is a function that every element can be mapped from element so that . In other words, every element of the function's codomain is the image of one element of ...

Ternary relation In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place. Just as a binary relat ...

Transitive relation In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive. Definition A ho ...

Trichotomy (mathematics) In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero.T ...

Well-founded relation In mathematics, a binary relation ''R'' is called well-founded (or wellfounded) on a class ''X'' if every non-empty subset ''S'' ⊆ ''X'' has a minimal element with respect to ''R'', that is, an element ''m'' not related by ''s ...

Mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

Set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

list A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby unio ...

Aleph null In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor and are named a ...

Bijection, injection and surjection In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which '' arguments'' (input expressions from the domain) and '' images'' (output expressions from the codomain) are related or ''m ...

Cantor's diagonal argument In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof, was published in 1891 by Georg Cantor as a m ...

Cantor's first uncountability proof Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties. One of these theorems is his "revolutionary discovery" that the set of all real numbers is unco ...

Cantor's theorem In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A, the set of all subsets of A, the power set of A, has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be ...

Cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. T ...

Codomain In mathematics, the codomain or set of destination of a function is the set into which all of the output of the function is constrained to fall. It is the set in the notation . The term range is sometimes ambiguously used to refer to either th ...

Constructible universe In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by , is a particular class of sets that can be described entirely in terms of simpler sets. is the union of the constructible hierarchy . It w ...

Continuum hypothesis In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to ...

Disjoint union In mathematics, a disjoint union (or discriminated union) of a family of sets (A_i : i\in I) is a set A, often denoted by \bigsqcup_ A_i, with an injection of each A_i into A, such that the images of these injections form a partition of A ( ...

Domain of a function In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by \operatorname(f) or \operatornamef, where is the function. More precisely, given a function f\colon X\to Y, the domain of is . ...

Element (mathematics) In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. Sets Writing A = \ means that the elements of the set are the numbers 1, 2, 3 and 4. Sets of elements of , for example \, are subsets o ...

Empty function In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the functi ...

Enumeration An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (fo ...

Extensionality In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned with whether the internal ...

Finite set In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, :\ is a finite set with five elements. T ...

Forcing (mathematics) In the mathematical discipline of set theory, forcing is a technique for proving consistency and independence results. It was first used by Paul Cohen in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Ze ...

Function (set theory) In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the functi ...

Generalized continuum hypothesis In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to ...

Index set In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set may be ''indexed'' or ''labeled'' by means of the elements of a set , then is an index set. The indexing consists ...

Infinite set In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Properties The set of natural numbers (whose existence is postulated by the axiom of infinity) is infinite. It is the only s ...

Inverse function In mathematics, the inverse function of a function (also called the inverse of ) is a function that undoes the operation of . The inverse of exists if and only if is bijective, and if it exists, is denoted by f^ . For a function f\colon X ...

Map (mathematics) In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: ''mapping'' the Earth surface to a sheet of paper. The term ''map'' may be used to distingu ...

Multiset In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that e ...

Naïve set theory Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It de ...

One-to-one correspondence In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other ...

Partition of a set In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a set defines a partition of this set, and every part ...

Pointed set In mathematics, a pointed set (also based set or rooted set) is an ordered pair (X, x_0) where X is a set and x_0 is an element of X called the base point, also spelled basepoint. Maps between pointed sets (X, x_0) and (Y, y_0) – called based ...

Power set In mathematics, the power set (or powerset) of a set is the set of all subsets of , including the empty set and itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is post ...

Projection (set theory) In set theory, a projection is one of two closely related types of functions or operations, namely: * A set-theoretic operation typified by the ''j''th projection map, written \mathrm_, that takes an element \vec = (x_1,\ \ldots,\ x_j,\ \ldots,\ x ...

Proper subset In mathematics, set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ...

Proper superset In mathematics, set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ...

Range of a function In mathematics, the range of a function may refer to either of two closely related concepts: * The codomain of the function * The image of the function Given two sets and , a binary relation between and is a (total) function (from to ) if ...

Russell's paradox In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains ...

Sequence (mathematics) In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...

Set (mathematics) A set is the mathematical model for a collection of different things; a set contains '' elements'' or ''members'', which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or ...

Set of all sets In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory inc ...

Superset In mathematics, set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ...

Tuple In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defi ...

Uncountable set In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal nu ...

Union (set theory) In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A refers to a union of ze ...

Von Neumann–Bernays–Gödel set theory In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces the notion of class, which is a colle ...

Zermelo set theory Zermelo set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory (ZF) and its extensions, such as von Neumann–Bernays–Gödel set theory (NBG). It be ...

Zermelo–Fraenkel set theory In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such ...

Metalogic Metalogic is the study of the metatheory of logic. Whereas ''logic'' studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems.Harry GenslerIntroduction to Logic Routledge, ...

metatheory A metatheory or meta-theory is a theory whose subject matter is theory itself, aiming to describe existing theory in a systematic way. In mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. ...

Completeness (logic) In mathematical logic and metalogic, a formal system is called complete with respect to a particular property (philosophy), property if every Well-formed formula, formula having the property can be formal proof, derived using that system, i.e. is ...

Consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...

Decidability (logic) In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems ar ...

Deductive system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A for ...

Interpretation (logic) An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning un ...

Cantor's theorem In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A, the set of all subsets of A, the power set of A, has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be ...

Church's thesis Church's is a high-end footwear manufacturer that was founded in 1873, by Thomas Church, in Northampton, England. In 1999 the company came under the control of Italian luxury fashion house Prada in a US$170 million deal. History Between the ...

Effective method In logic, mathematics and computer science, especially metalogic and computability theory, an effective method Hunter, Geoffrey, ''Metalogic: An Introduction to the Metatheory of Standard First-Order Logic'', University of California Press, 1971 or ...

Formal system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...

Gödel's completeness theorem Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem applies to any first-order theory: ...

Independence (mathematical logic) In mathematical logic, independence is the unprovability of a sentence from other sentences. A sentence σ is independent of a given first-order theory ''T'' if ''T'' neither proves nor refutes σ; that is, it is impossible to prove σ from ''T' ...

Metasyntactic variable A metasyntactic variable is a specific word or set of words identified as a placeholder in computer science and specifically computer programming. These words are commonly found in source code and are intended to be modified or substituted before ...

Metatheorem In logic, a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metathe ...

Symbol (formal) A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other ...

Type–token distinction The type–token distinction is the difference between naming a ''class'' (type) of objects and naming the individual ''instances'' (tokens) of that class. Since each type may be exemplified by multiple tokens, there are generally more tokens than ...

Use–mention distinction The use–mention distinction is a foundational concept of analytic philosophy, according to which it is necessary to make a distinction between a word (or phrase) and it.Devitt and Sterelny (1999) pp. 40–1W.V. Quine (1940) p. 24 Many philos ...

Well-formed formula In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can ...

deductive apparatus A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...

Deductive system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A for ...

Formal proof In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the seq ...

Formal system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...

Interpretation (logic) An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning un ...

Model A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

Semantic consequence Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...

Truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Computing In some pro ...

Turing degree In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set. Overview The concept of Turing degree is fund ...

Alpha recursion theory In recursion theory, α recursion theory is a generalisation of recursion theory to subsets of admissible ordinals \alpha. An admissible set is closed under \Sigma_1(L_\alpha) functions, where L_\xi denotes a rank of Godel's constructible hierarchy ...

Arithmetical set In mathematical logic, an arithmetical set (or arithmetic set) is a set of natural numbers that can be defined by a formula of first-order Peano arithmetic. The arithmetical sets are classified by the arithmetical hierarchy. The definition can be ...

Computable function Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do ...

Decision problem In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm wheth ...

Effective method In logic, mathematics and computer science, especially metalogic and computability theory, an effective method Hunter, Geoffrey, ''Metalogic: An Introduction to the Metatheory of Standard First-Order Logic'', University of California Press, 1971 or ...

Entscheidungsproblem In mathematics and computer science, the ' (, ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "Yes" or "No" according to whether the state ...

Enumeration An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (fo ...

Halting problem In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a ...

List of undecidable problems In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is, any possible program would som ...

Post correspondence problem The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946. Because it is simpler than the halting problem and the ''Entscheidungsproblem'' it is often used in proofs of undecidability. Definiti ...

Post's theorem In computability theory Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. Background The statement of Post's theorem uses several concepts relating to definability and ...

Primitive recursive function In computability theory, a primitive recursive function is roughly speaking a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop can be determined ...

Recursive language In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the ...

Recursive set In computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as input, terminates after a finite amount of time (possibly depending on the given number) and correctly ...

Recursively enumerable language In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set o ...

Recursively enumerable set In computability theory, a set ''S'' of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable, provable or Turing-recognizable if: *There is an algorithm such that th ...

Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...

Alternative semantics Alternative semantics (or Hamblin semantics) is a framework in formal semantics and logic. In alternative semantics, expressions denote ''alternative sets'', understood as sets of objects of the same semantic type. For instance, while the word "Le ...

Categorial grammar Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and seman ...

Combinatory categorial grammar Combinatory categorial grammar (CCG) is an efficiently parsable, yet linguistically expressive grammar formalism. It has a transparent interface between surface syntax and underlying semantic representation, including predicate–argument structur ...

Discourse representation theory In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT inclu ...

Dynamic semantics Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dynam ...

Inquisitive semantics Inquisitive semantics is a framework in logic and natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both the information that the sentence conveys and the issue that it raises. The framework provides ...

Compositionality In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. ...

Generalized quantifier In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases. For example, the generalized quantifier ''every boy'' denotes the set of sets of ...

Modality (natural language) In linguistics and philosophy, modality refers to the ways language can express various relationships to reality or truth. For instance, a modal expression may convey that something is likely, desirable, or permissible. Quintessential modal ex ...

Opaque context An opaque context or referentially opaque context is a linguistic context in which it is not always possible to substitute "co-referential" expressions (expressions referring to the same object) without altering the truth of sentences. The expres ...

Propositional attitudes A propositional attitude is a mental state held by an agent toward a proposition. Linguistically, propositional attitudes are denoted by a verb (e.g. "believed") governing an embedded "that" clause, for example, 'Sally believed that she had won ...

Scope (formal semantics) In formal semantics, the scope of a semantic operator is the semantic object to which it applies. For instance, in the sentence "''Paulina doesn't drink beer but she does drink wine''," the proposition that Paulina drinks beer occurs within the sco ...

Type shifter Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * ...

Vagueness In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is ...

Law of the excluded middle In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradi ...

Double negation elimination In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition ''A'' is logically equivalent to ''not (not ...

Law of noncontradiction In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the sa ...

Principle of explosion In classical logic, intuitionistic logic and similar logical systems, the principle of explosion (, 'from falsehood, anything ollows; or ), or the principle of Pseudo-Scotus, is the law according to which any statement can be proven from a ...

Monotonicity of entailment Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this property can be captured by an inference rule called ...

De Morgan duality In propositional calculus, propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both Validity (logic), valid rule of inference, rules of inference. They are na ...

logical operator In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...

Term logic In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...

Baroco In Aristotelian logic, baroco is a mnemonic word used to memorize a syllogism. Specifically, it has the first proposition universal and affirmative, but the second and third particular and negative, and the middle term the attribute in the two firs ...

Boolean-valued function A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = ), whose elements are i ...

Distribution of terms In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the ''subject term'') are included in another (the ''predicate term''). The study of arguments ...

Enthymeme An enthymeme ( el, ἐνθύμημα, ''enthýmēma'') is a form of rational appeal, or deductive argument. It is also known as a rhetorical syllogism and is used in oratorical practice. While the syllogism is used in dialectic, or the art of log ...

Immediate inference An immediate inference is an inference which can be made from only one statement or proposition. For instance, from the statement "All toads are green", the immediate inference can be made that "no toads are not green" or "no toads are non-green" ...

Logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...

Logical hexagon Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

Major term A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

Middle term In logic, a middle term is a term that appears (as a subject or predicate of a categorical proposition) in both premises but not in the conclusion of a categorical syllogism. Example: :Major premise: All men are mortal. :Minor premise A syllogi ...

Minor term A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

Organon The ''Organon'' ( grc, Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic. The name ''Organon'' was given by Aristotle's followers, the Peripatetics. The six ...

Port-Royal Logic ''Port-Royal Logic'', or ''Logique de Port-Royal'', is the common name of ''La logique, ou l'art de penser'', an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jan ...

Premise A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agre ...

Relative term A relative term is a term that makes two or more distinct references to objects (which may be the same object, for example in "The Morning Star is the Evening Star"). A relative term is typically expressed in ordinary language by means of a phrase ...

Sorites paradox The sorites paradox (; sometimes known as the paradox of the heap) is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually. With the assumption that removing a sing ...

Tetralemma The tetralemma is a figure that features prominently in the logic of India. Definition It states that with reference to any a logical proposition X, there are four possibilities: : X (affirmation) : \neg X (negation) : X \land\neg X (both) : \n ...

Truth function In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly o ...

Alethic logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

Deontic logic Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It ...

Doxastic logic Doxastic logic is a type of logic concerned with reasoning about beliefs. The term ' derives from the Ancient Greek (''doxa'', "opinion, belief"), from which the English term '' doxa'' ("popular opinion or belief") is also borrowed. Typically, a ...

Epistemic logic Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applica ...

Temporal logic In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I ...

Non-classical logic Non-classical logics (and sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done, including by way of ...

Affine logic Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linear logic with weakening. The name "affine logic" is associated with linear logic, to which it differs by all ...

Decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...

Deviant logic Deviant logic is a type of logic incompatible with classical logic. Philosopher Susan Haack uses the term ''deviant logic'' to describe certain non-classical systems of logic. In these logics: * the set of well-formed formulas generated equals th ...

Intensional logic Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe (''extensions''), by additional quantifiers that range over terms that may have such individuals ...

Intuitionistic logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems ...

Many-valued logic Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false ...

Minimal logic Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson. It is an intuitionistic and paraconsistent logic, that rejects both the law of the excluded middle as well as the principle of explosion ...

Non-monotonic logic A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reasoning), i.e., a kind of inference in which re ...

Probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

Quantum logic In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The field takes as its starting point an observ ...

Relevance logic Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but ...

Substructural logic In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening, contraction, exchange or associativity. Two of the more significant substructural logics are r ...

Mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

Set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

Formal system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...

Predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

Predicate Predicate or predication may refer to: * Predicate (grammar), in linguistics * Predication (philosophy) * several closely related uses in mathematics and formal logic: **Predicate (mathematical logic) **Propositional function **Finitary relation, o ...

Higher-order logic mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more express ...

Propositional calculus Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations ...

Proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...

Truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Computing In some pro ...

Venn diagram A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships ...

Infinitary logic An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In particular, infinitary logics may fail to be co ...

Categorical logic __NOTOC__ Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. In broad terms, categ ...

Metalogic Metalogic is the study of the metatheory of logic. Whereas ''logic'' studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems.Harry GenslerIntroduction to Logic Routledge, ...

Temporal logic In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I ...

Sequential logic In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past inputs, the input history. This is in contrast to ''combinational logic'', whose output i ...

Provability logic Provability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as Peano arithmetic. Examples ...

Interpretability In mathematical logic, interpretability is a relation between formal theories that expresses the possibility of interpreting or translating one into the other. Informal definition Assume ''T'' and ''S'' are formal theories. Slightly simplified, '' ...

Quantum logic In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The field takes as its starting point an observ ...

Relevant logic Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but ...

Consequent A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if ''P'' implies ''Q'', then ''P'' is called the antecedent and ''Q'' is called ...

Affirming the consequent Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dar ...

Denying the antecedent Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form: :If ''P'', then ''Q''. :Therefore, if not ...

Theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of t ...

Axiomatic system In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains ...

Conditional proof A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent. Overview The assumed antecedent of a conditional proof is called the conditio ...

Truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as belie ...

Truth condition In semantics and pragmatics, a truth condition is the condition under which a sentence is true. For example, "It is snowing in Nebraska" is true precisely when it is snowing in Nebraska. Truth conditions of a sentence do not necessarily reflect cu ...

Truth function In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly o ...

Double negation In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition ''A'' is logically equivalent to ''not (not ...

Double negation elimination In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition ''A'' is logically equivalent to ''not (not ...

Existential fallacy The existential fallacy, or existential instantiation, is a formal fallacy. In the existential fallacy, one presupposes that a class has members when one is not supposed to do so; i.e., when one should not assume existential import. Not to be c ...

Logical fallacy In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic syst ...

Syllogistic fallacy A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. ...

Type theory In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a fou ...

Game semantics Game semantics (german: dialogische Logik, translated as ''dialogical logic'') is an approach to Formal semantics (logic), formal semantics that grounds the concepts of truth or Validity (logic), validity on game theory, game-theoretic concepts, su ...

Inference rule In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of ...

Law of excluded middle In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradi ...

Law of non-contradiction In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the sa ...

Logical constant In logic, a logical constant of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal. Two important types of logical constants are logical connectives and quantifiers. The equality predicate (us ...

Logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...

Boolean Function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...

Logical assertion In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order logic would be ''that a string is a well-formed formula'', or ''that a proposition is tru ...

Logical conditional Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

Logical biconditional In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective (\leftrightarrow) used to conjoin two statements and to form the statement " if and only if ", where is known as th ...

Logical equivalence In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending o ...

Logical AND In logic, mathematics and linguistics, And (\wedge) is the truth-functional operator of logical conjunction; the ''and'' of a set of operands is true if and only if ''all'' of its operands are true. The logical connective that represents this ...

Logical OR In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S ...

Logical NAND In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called nand ("not and") or ...

Contradiction In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's ...

Logicism In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all ...

Hypothetical syllogism In classical logic, a hypothetical syllogism is a valid argument form, a syllogism with a conditional statement for one or both of its premises. An example in English: :If I do not wake up, then I cannot go to work. :If I cannot go to work, then ...

Minor premise A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

Term Term may refer to: * Terminology, or term, a noun or compound word used in a specific context, in particular: **Technical term, part of the specialized vocabulary of a particular field, specifically: ***Scientific terminology, terms used by scient ...

Singular term A singular term is a paradigmatic referring device in a language. Singular terms are of philosophical importance for philosophers of language, because they ''refer'' to things in the world, and the ability of words to refer calls for scrutiny. Ove ...

Major term A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

Middle term In logic, a middle term is a term that appears (as a subject or predicate of a categorical proposition) in both premises but not in the conclusion of a categorical syllogism. Example: :Major premise: All men are mortal. :Minor premise A syllogi ...

Soundness In logic or, more precisely, deductive reasoning, an argument is sound if it is both valid in form and its premises are true. Soundness also has a related meaning in mathematical logic, wherein logical systems are sound if and only if every formu ...

Inverse (logic) In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form P \rightarrow Q , the inverse refers to the sentence \neg P ...

Satisfiability In mathematical logic, a formula is ''satisfiable'' if it is true under some assignment of values to its variables. For example, the formula x+3=y is satisfiable because it is true when x=3 and y=6, while the formula x+1=x is not satisfiable over ...

Logical language Engineered languages (often abbreviated to engelangs, or, less commonly, engilangs) are constructed languages devised to test or prove some hypotheses about how languages work or might work. There are at least three subcategories, philosophical ...

Paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

Polish notation Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators ''precede'' their operands, in contrast ...

Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...

Reductio ad absurdum In logic, (Latin for "reduction to absurdity"), also known as (Latin for "argument to absurdity") or ''apagogical arguments'', is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absu ...

Necessary and sufficient In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of ...

Nonfirstorderizability In formal logic, nonfirstorderizability is the inability of a natural-language statement to be adequately captured by a formula of first-order logic. Specifically, a statement is nonfirstorderizable if there is no formula of first-order logic whic ...

Socratic method The Socratic method (also known as method of Elenchus, elenctic method, or Socratic debate) is a form of cooperative argumentative dialogue between individuals, based on asking and answering questions to stimulate critical thinking and to draw ou ...

Logic programming Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic pro ...

History of logic The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic (or term logic) as found ...

Journal of Logic, Language and Information The ''Journal of Logic, Language and Information'' is a quarterly peer-reviewed academic journal covering research on "natural, formal, and programming languages". It is the official journal of the European Association for Logic, Language and Infor ...

Linguistics and Philosophy ''Linguistics and Philosophy'' is a peer-reviewed journal addressing "structure and meaning in natural language". This journal, along with '' Studies in Language'', is a continuation of the journal ''Foundations of Language'' (1965 to 1976). The ...

A System of Logic ''A System of Logic, Ratiocinative and Inductive'' is an 1843 book by English philosopher John Stuart Mill. Overview In this work, he formulated the five principles of inductive reasoning that are known as Mill's Methods. This work is important ...

Begriffsschrift ''Begriffsschrift'' (German for, roughly, "concept-script") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. ''Begriffsschrift'' is usually translated as ''concept writing'' or ''concept notatio ...

Categories (Aristotle) The ''Categories'' ( Greek Κατηγορίαι ''Katēgoriai''; Latin ''Categoriae'' or ''Praedicamenta'') is a text from Aristotle's '' Organon'' that enumerates all the possible kinds of things that can be the subject or the predicate of a p ...

Charles Sanders Peirce bibliography This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and . For an extensive chronological list of Peirce's works (titled in English), s ...

Laws of Form ''Laws of Form'' (hereinafter ''LoF'') is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. ''LoF'' describes three distinct logical systems: * The "primary arithmetic" (described in C ...

Novum Organum The ''Novum Organum'', fully ''Novum Organum, sive Indicia Vera de Interpretatione Naturae'' ("New organon, or true directions concerning the interpretation of nature") or ''Instaurationis Magnae, Pars II'' ("Part II of The Great Instauration ...

On Formally Undecidable Propositions of Principia Mathematica and Related Systems "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I" ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") is a paper in mathematical logic by Kurt Gödel. Submitted November ...

Organon The ''Organon'' ( grc, Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic. The name ''Organon'' was given by Aristotle's followers, the Peripatetics. The six ...

Port-Royal Logic ''Port-Royal Logic'', or ''Logique de Port-Royal'', is the common name of ''La logique, ou l'art de penser'', an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jan ...

Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...

Sophistical Refutations ''Sophistical Refutations'' ( el, Σοφιστικοὶ Ἔλεγχοι, Sophistikoi Elenchoi; la, De Sophisticis Elenchis) is a text in Aristotle's ''Organon'' in which he identified thirteen fallacies.Sometimes listed as twelve. According to A ...

The Art of Being Right ''The Art of Being Right: 38 Ways to Win an Argument'' (also ''The Art of Controversy'', or ''Eristic Dialectic: The Art of Winning an Argument''; German: ''Eristische Dialektik: Die Kunst, Recht zu behalten''; 1831) is an acidulous, sarcastic tre ...

Tractatus Logico-Philosophicus The ''Tractatus Logico-Philosophicus'' (widely abbreviated and cited as TLP) is a book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein which deals with the relationship between language and reality and aims to define th ...

Association for Symbolic Logic The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Alonzo Church. The current president of the ASL is ...

List of logicians A logician is a person who studies logic. Some famous logicians are listed below in English alphabetical transliteration order (by surname). __NOTOC__ A * Peter Abelard (France, 1079–1142) * Wilhelm Ackermann (Germany, 1896–1962) * Serge ...

Peter Suber Peter Dain Suber (born November 8, 1951) is a philosopher specializing in the philosophy of law and open access to knowledge. He is a Senior Researcher at the Berkman Klein Center for Internet & Society, Director of the Harvard Office for Scholarl ...

Logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

Foundations of logic

Branches of logic

Philosophical logic

Informal logic and critical thinking

Deductive reasoning

Theories of deduction

Fallacies

Formal logic

Symbols and strings of symbols

Logical symbols

= Logical connectives

Strings of symbols

Types of propositions

= Rules of inference

Formal theories

Expressions in a metalanguage

Propositional and boolean logic

Propositional logic

Boolean logic

Predicate logic and relations

Predicate logic

Relations

Mathematical logic

Set theory

Metalogic

Proof theory

Model theory

Computability theory

Semantics of natural language

Classical logic

Modal logic

Non-classical logic

Concepts of logic

History of logic

Literature about logic

Journals

Books

Logic organizations

Logicians

See also

External links