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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 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-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 inquisitive proposition \ encodes that the actual ... [...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 science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...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 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 maximal/mi ... [...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 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) 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 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 computerized proof methods may not use classical logic i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ..., linguistics and computer science. History In English, the study of meaning in language has been known by many names that involve the Ancient Greek word (''sema'', "sign, mark, token"). In 1690, a Greek rendering of the term ''semiotics'', the interpretation of signs and symbols, finds an early allusion in John Locke's ''An Essay Concerning Human Understanding'': The third Branch may be called [''simeiotikí'', "semiotics"], or the Doctrine of Signs, the most usual whereof being words, it is aptly enough ter ... [...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? This feature exists, for example, in English and Russian. 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 t ... [...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 wonders 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. Questi ... [...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. ''Polar questions'' are those such as the English language, English example "Is this a polar question?", which can be answered with "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 which raise an issue to be resol ... [...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 all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 S , assuming that R abbreviates "it is raining" and S abbreviates "it is snowing". 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 including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well t ... [...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, NPIs, presupposition, and implicature In pragmatics, a subdiscipline of linguistics, an implicature is something the speaker suggests or implies with an utterance, even though it is not litera ... [...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 maximal/mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
