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Logical Form
In logic, the 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, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language. The logical form of an argument is called the argument form of the argument. History The importance of the concept of form to logic was already recognized in ancient times. Aristotle, in the '' Prior Analytics'', was one of the first people to employ variable letters to represent valid inferences. Therefore, Jan Łukasiewicz claims that the introduction of variables was "one of Aristotle's greatest inventions." ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Reasoning
Inductive reasoning refers to a variety of method of reasoning, methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but with some degree of probability. Unlike Deductive reasoning, ''deductive'' reasoning (such as mathematical induction), where the conclusion is ''certain'', given the premises are correct, inductive reasoning produces conclusions that are at best ''probable'', given the evidence provided. Types The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded. Inductive generalization A generalization (more accurately, an ''inductive generalization'') proceeds from premises about a Sample (statistics), sample to a conclusion about the statistical population, population. The observation obtained from this sample is projected onto the broader population. : The proportion Q of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copula (linguistics)
In linguistics, a copula (; : copulas or copulae; abbreviated ) is a word or phrase that links the subject of a sentence to a subject complement, such as the word ''is'' in the sentence "The sky is blue" or the phrase ''was not being'' in the sentence "It was not being cooperative." The word ''copula'' derives from the Latin noun for a "link" or "tie" that connects two different things. A copula is often a verb or a verb-like word, though this is not universally the case. A verb that is a copula is sometimes called a copulative or copular verb. In English primary education grammar courses, a copula is often called a linking verb. In other languages, copulas show more resemblances to pronouns, as in Classical Chinese and Guarani, or may take the form of suffixes attached to a noun, as in Korean, Beja, and Inuit languages. Most languages have one main copula (in English, the verb "to be"), although some (such as Spanish, Portuguese and Thai) have more than one, while ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schematic 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 sentences of a language ℒ'' the symbols A and B are part of the metalanguage in which the statement about the object language ℒ is formulated. John Corcoran considered this terminology unfortunate because it obscures the use of schemata and because such "variables" do not actually range over a domain. The convention is that a metavariable is to be uniformly substituted with the same instance in all its appearances in a given schema. This is in contrast with nonterminal symbols in formal grammars where the nonterminals on the right of a production can be substituted by different instances.. Attempts to formalize the notion of metavariable result in some kind of type theory In mathematics and theoretical computer science, a type theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Informal Logic
Informal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements). However, the precise definition of "informal logic" is a matter of some dispute. Ralph H. Johnson and J. Anthony Blair define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation."Johnson, Ralph H., and Blair, J. Anthony (1987), "The Current State of Informal Logic", ''Informal Logic'', 9(2–3), 147–151. Johnson & Blair added "... in everyday discourse" but in (2000), modified their definition, and broadened the focus now to include the sorts of argument that occurs not just in everyday discourse but also disciplined inquiry—what Weinstein (1990) calls "stylized discourse." This definition reflects what had been implicit in their practice and what others were doing in their informal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argumentation Theory
Argumentation theory 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 includes the arts and sciences of civil debate, dialogue, conversation, and persuasion. It studies rules of inference, logic, and procedural rules in both artificial and real-world settings. Argumentation includes various forms of dialogue such as deliberation and negotiation which are concerned with collaborative decision-making procedures. It also encompasses eristic dialogue, the branch of social debate in which victory over an opponent is the primary goal, and didactic dialogue used for teaching. This discipline also studies the means by which people can express and rationally resolve or at least manage their disagreements. Argumentation is a daily occurrence, such as in public debate, science, and law. For example in law, in courts by the judge, the partie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. The principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the principle has never been explicitly stated by Frege, and arguably it was already assumed by George Boole decades before Frege's work. The principle of compositionality (also known as semantic compositionalism) is highly debated in linguistics. Among its most challenging problems there are the issues of contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations. History Discussion of compositionality started to appear at the beginning of the 19th century, during which it was debated whether what was most fundamental in language was compositionalit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordered Set
In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word ''partial'' is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered pair P=(X,\leq) consisting of a set X (called the ''ground set'' of P) and a partial order \leq on X. When the meaning is clear from context and there is no ambiguity about the partial order, the set X itself is sometimes called a poset. Partial order relations The term ''partial order'' usually refers to the reflexive partial order relations, referred to in this article as ''non-strict'' partial orders. However some a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denying The Antecedent
Denying the antecedent (also known as inverse error or fallacy of the inverse) is a formal fallacy of inferring the inverse from an original statement. Phrased another way, denying the antecedent occurs in the context of an indicative conditional statement and assumes that the negation of the antecedent implies the negation of the consequent. It is a type of mixed hypothetical syllogism that takes on the following form: :If ''P'', then ''Q''. :Not ''P''. :Therefore, not ''Q''. which may also be phrased as :P \rightarrow Q (P implies Q) :\therefore \neg P \rightarrow \neg Q (therefore, not-P implies not-Q) Arguments of this form are invalid. Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true. The name ''denying the antecedent'' derives from the premise "not ''P''", which denies the "if" clause (antecedent) of the conditional premise. The only situation where one may deny the an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affirming The Consequent
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the antecedent is true. It takes on the following form: :: If ''P'', then ''Q''. :: ''Q''. :: Therefore, ''P''. which may also be phrased as : P \rightarrow Q (P implies Q) : \therefore Q \rightarrow P (therefore, Q implies P) For example, it may be true that a broken lamp would cause a room to become dark. It is not true, however, that a dark room implies the presence of a broken lamp. There may be no lamp (or any light source). The lamp may also be off. In other words, the consequent (a dark room) can have other antecedents (no lamp, off-lamp), and so can still be true even if the stated antecedent is not. Converse errors are comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Tollens
In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "mode that by denying denies") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens'' is a mixed hypothetical syllogism that takes the form of "If ''P'', then ''Q''. Not ''Q''. Therefore, not ''P''." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from ''P implies Q'' to ''the negation of Q implies the negation of P'' is a valid argument. The history of the inference rule ''modus tollens'' goes back to antiquity. The first to explicitly describe the argument form ''modus tollens'' was Theophrastus. ''Modus tollens'' is closely related to ''modus ponens''. There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive. Explanation The form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Ponens
In propositional logic, (; MP), also known as (), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "''P'' implies ''Q.'' ''P'' is true. Therefore, ''Q'' must also be true." ''Modus ponens'' is a mixed hypothetical syllogism and is closely related to another valid form of argument, '' modus tollens''. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of ''modus ponens''. The history of ''modus ponens'' goes back to antiquity. The first to explicitly describe the argument form ''modus ponens'' was Theophrastus. It, along with '' modus tollens'', is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal. Explanation The form of a ''modus ponens'' argument is a mixed hypothetical syllogism, with two premises and a con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
