|
Inquisitive Semantics
Inquisitive semantics is a framework in logic and Formal semantics (linguistics), 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 a foundation for the linguistic analysis of statements and questions. It was originally developed by Ivano Ciardelli, Jeroen Groenendijk, Salvador Mascarenhas, and Floris Roelofsen. Basic notions The essential notion in inquisitive semantics is that of an ''inquisitive proposition''. * An ''information state'' (alternately a ''classical proposition'') is a set of possible worlds. * An ''inquisitive proposition'' is a nonempty downward closure, downward-closed set of information states. Inquisitive propositions encode informational content via the region of logical space that their information states cover. For instance, the inquisitive proposition \ encodes the information that is the actual world. The ... [...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] |
Join (mathematics)
In mathematics, specifically order theory, the join of a subset S of a partially ordered set P is the supremum (least upper bound) of S, denoted \bigvee S, and similarly, the meet of S is the infimum (greatest lower bound), denoted \bigwedge S. In general, the join and meet of a subset of a partially ordered set need not exist. Join and meet are Duality (order theory), dual to one another with respect to order inversion. A partially ordered set in which all pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that is both a join-semilattice and a meet-semilattice is a Lattice (order), lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or join but the operations (when defined) satisfy certain axioms. The join/meet of a subset of a Tot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systems Of Formal Logic
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term ''system'' comes from the Latin word ''systēma'', in turn from Greek ''systēma'': "whole concept made of several parts or members, system", literary "composition"."σύστημα" , Henry George Liddell, Robert Scott, '' |
Non-classical Logic
Non-classical logics (and sometimes alternative logics or non-Aristotelian 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 commonly the case, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth. Philosophical logic is understood to encompass and focus on non-classical logics, although the term has other meanings as well. In addition, some parts of theoretical computer science can be thought of as using non-classical reasoning, although this varies according to the subject area. For example, the basic boolean functions (e.g. AND, OR, NOT, etc) in computer science are very much classical in nature, as is clearly the case given that they can be fully described by classical truth tables. However, in contrast, some computeriz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics
Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction between sense and reference. Sense is given by the ideas and concepts associated with an expression while reference is the object to which an expression points. Semantics contrasts with syntax, which studies the rules that dictate how to create grammatically correct sentences, and pragmatics, which investigates how people use language in communication. Lexical semantics is the branch of semantics that studies word meaning. It examines whether words have one or several meanings and in what lexical relations they stand to one another. Phrasal semantics studies the meaning of sentences by exploring the phenomenon of compositionality or how new meanings can be created by arranging words. Formal semantics (natural language), Formal semantics relies o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rising Declarative
In linguistics, a rising declarative is an utterance which has the syntactic form of a declarative but the rising intonation typically associated with polar interrogatives. # ''Rising declarative:'' Justin Bieber wants to hang out with me? # ''Falling declarative:'' Justin Bieber wants to hang out with me. # ''Polar question'': Does Justin Bieber want to hang out with me? Research on rising declaratives has suggested that they fall into two categories, ''assertive rising declaratives'' and ''inquisitive rising declaratives''. These categories are distinguished both by the particulars of their pitch contours and their conventional discourse effects. However, the distinction in pitch contour is not categorical, varying between speakers and overridable by context. Assertive rising declaratives are characterized phonologically by a high pitch accent which rises to a high boundary tone, notated as H* H-H% in the ToBI system. Assertive rising declaratives are assertio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Responsive Predicate
In formal semantics a responsive predicate is an embedding predicate which can take either a declarative or an interrogative complement. For instance, the English verb ''know'' is responsive as shown by the following examples. # Bill knows whether Mary left. # Bill knows that Mary left. Responsives are contrasted with ''rogatives'' such as ''wonder'' which can only take an interrogative complement and ''anti-rogatives'' such as ''believe'' which can only take a declarative complement. # Bill wonders whether Mary left. # *Bill wonders that Mary left. # *Bill believes whether Mary left. # Bill believes that Mary left. Some analyses have derived these distinctions from type compatibility while others explain them in terms of particular properties of the embedding verbs and their complements. See also * Embedded clause * Propositional attitude * Inquisitive semantics * Interrogative clause * Question A question is an utterance which serves as a request for information ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Question
A question is an utterance which serves as a request for information. Questions are sometimes distinguished from interrogatives, which are the grammar, grammatical forms, typically used to express them. Rhetorical questions, for instance, are interrogative in form but may not be considered wiktionary:bona fide, bona fide questions, as they are not expected to be answered. Questions come in a number of varieties. For instance; ''Polar questions'' are those such as the English language, English example "Is this a polar question?", which can be answered with yes and no, "yes" or "no". ''Alternative questions'' such as "Is this a polar question, or an alternative question?" present a list of possibilities to choose from. ''Open-ended question, Open questions'' such as "What kind of question is this?" allow many possible resolutions. Questions are widely studied in linguistics and philosophy of language. In the subfield of pragmatics, questions are regarded as illocutionary acts whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 logics (the logics are intermediate between intuitionistic logic and classical logic).. Definition A superintuitionistic logic is a set ''L'' of propositional formulas in a countable set of variables ''p''''i'' satisfying the following properties: :1. all axioms of intuitionistic logic belong to ''L''; :2. if ''F'' and ''G'' are formulas such that ''F'' and ''F'' → ''G'' both belong to ''L'', then ''G'' also belongs to ''L'' (closure under modus ponens); :3. if ''F''(''p''1, ''p''2, ..., ''p''''n'') is a formula of ''L'', and ''G''1, ''G''2, ..., ''G''''n'' are any formulas, then ''F''(''G''1, ''G''2, ..., ''G''''n'') belongs to ''L'' (closure under substitution). Such a logic is intermediate if furthermore :4. ''L'' is not the set of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disjunction
In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula S \lor W , assuming that S abbreviates "it is sunny" and W abbreviates "it is warm". In classical logic, disjunction is given a truth functional semantics according to which a formula \phi \lor \psi is true unless both \phi and \psi are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an ''inclusive'' interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 "Lena" might denote Lena herself in a classical semantics, it would denote the singleton set containing Lena in alternative semantics. The framework was introduced by Charles Leonard Hamblin in 1973 as a way of extending Montague grammar to provide an analysis for questions. In this framework, a question denotes the set of its possible answers. Thus, if P and Q are propositions, then \ is the denotation of the question whether P or Q is true. Since the 1970s, it has been extended and adapted to analyze phenomena including focus, scope, disjunction In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as \lor and read aloud as "o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meet (mathematics)
In mathematics, specifically order theory, the join of a subset S of a partially ordered set P is the supremum (least upper bound) of S, denoted \bigvee S, and similarly, the meet of S is the infimum (greatest lower bound), denoted \bigwedge S. In general, the join and meet of a subset of a partially ordered set need not exist. Join and meet are dual to one another with respect to order inversion. A partially ordered set in which all pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or join but the operations (when defined) satisfy certain axioms. The join/meet of a subset of a totally ordered set is simply the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
