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Free Choice Inference
Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie ''AND'' that they can also play video games, depending on their preference: # You can watch a movie OR play video games. # You can watch a movie OR you can play video games. Free choice inferences are a major topic of research in formal semantics and philosophical logic because they are not valid in classical systems of modal logic. If they were valid, then the semantics of natural language would validate the ''Free Choice Principle''. # ''Free Choice Principle'': (\Diamond P \lor \Diamond Q) \rightarrow (\Diamond P \land \Diamond Q) This symbolic logic formula above is not valid in classical modal logic: Adding this principle as an axiom to standard modal logics would allow one to conclude ... [...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 wel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indefinite Article
An article is any member of a class of dedicated words that are used with noun phrases to mark the identifiability of the referents of the noun phrases. The category of articles constitutes a part of speech. In English, both "the" and "a(n)" are articles, which combine with nouns to form noun phrases. Articles typically specify the grammatical definiteness of the noun phrase, but in many languages, they carry additional grammatical information such as gender, number, and case. Articles are part of a broader category called determiners, which also include demonstratives, possessive determiners, and quantifiers. In linguistic interlinear glossing, articles are abbreviated as . Types Definite article A definite article is an article that marks a definite noun phrase. Definite articles such as English '' the'' are used to refer to a particular member of a group. It may be something that the speaker has already mentioned or it may be otherwise something uniquely specifie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Logic
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic. An important issue for philosophical logic is the question of how to classify the great variety of non-classical logical systems, many of which are of rather recent origin. One form of classification often found in the literature is to distinguish between extended logics and deviant logics. Logic itself can be defined as 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 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 usua ... [...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, 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 termed also , Logick. In 1831, the term is suggested for the third branch of division of knowledge akin to Locke; the "signs of our knowledge". In 1857, the term '' semasiology'' (borrowed from German ''Semasiologie'') is attested in Josiah W. Gibb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sluicing
In syntax, sluicing is a type of Ellipsis (linguistics), ellipsis that occurs in both direct and indirect interrogative clauses. The ellipsis is introduced by a ''wh''-expression, whereby in most cases, everything except the ''wh''-expression is elided from the clause. Sluicing has been studied in detail in the early 21st century and it is therefore a relatively well-understood type of ellipsis. Sluicing occurs in many languages.See Merchant's (2001) extensive account of sluicing; it includes examples from numerous languages. Basic examples Sluicing is illustrated with the following examples. In each case, an embedded question is understood though only a question word or phrase is pronounced. (The intended interpretations of the question-denoting elliptical clause are given in parentheses; parts of these are anaphoric to the boldface material in the antecedent.) ::Phoebe ate something, but she doesn't know what. (=what she ate) ::Jon doesn't like the lentils, but he doesn't know ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simplification Of Disjunctive Antecedents
In formal semantics and philosophical logic, simplification of disjunctive antecedents (SDA) is the phenomenon whereby a disjunction in the antecedent of a conditional appears to distribute over the conditional as a whole. This inference is shown schematically below: # (A \lor B) \Rightarrow C \models (A \Rightarrow C) \land (B \Rightarrow C) This inference has been argued to be valid on the basis of sentence pairs such as that below, since Sentence 1 seems to imply Sentence 2. # If Yde or Dani had come to the party, it would have been fun. # If Yde had come to the party, it would be been fun and if Dani had come to the party, it would have been fun. The SDA inference was first discussed as a potential problem for the similarity analysis of counterfactuals. In these approaches, a counterfactual (A \lor B) > C is predicted to be true if C holds throughout the possible worlds where A \lor B holds which are most similar to the world of evaluation. On a Boolean semantics fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ross's Paradox
Imperative logic is the field of logic concerned with imperatives. In contrast to declaratives, it is not clear whether imperatives denote propositions or more generally what role truth and falsity play in their semantics. Thus, there is almost no consensus on any aspect of imperative logic. Jørgensen's dilemma One of a logic's principal concerns is logical validity. It seems that arguments with imperatives can be valid. Consider: :P1. Take all the books off the table! :P2. ''Foundations of Arithmetic'' is on the table. :C1. Therefore, take ''Foundations of Arithmetic'' off the table! However, an argument is valid if the conclusion follows from the premises. This means the premises give us reason to believe the conclusion, or, alternatively, the truth of the premises determines truth of the conclusion. Since imperatives are neither true nor false and since they are not proper objects of belief, none of the standard accounts of logical validity apply to arguments containing im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal 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 systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a '' possible world''. A formula's truth value ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Kamp
Johan Anthony Willem "Hans" Kamp (born 5 September 1940) is a Dutch philosopher and Linguistics, linguist, responsible for introducing discourse representation theory (DRT) in 1981. Kamp was born in Den Burg. He received a Ph.D. in UCLA Department of Philosophy, Philosophy from UCLA in 1968, and has taught at Cornell University, University of London, University of Texas, Austin, and University of Stuttgart. His dissertation, ''Tense Logic and the Theory of Linear Order'' (1968) was devoted to functional completeness in tense logic, the main result being that all temporal operators are definable in terms of "since" and "until", provided that the underlying temporal structure is a continuous Total order, linear ordering. Kamp's 1971 paper on "now" (published in ''Theoria (philosophy journal), Theoria'') was the first employment of double-indexing in model theory, model theoretic semantics. His doctoral committee included Richard Montague as chairman, Chen Chung Chang, Alonzo Church, ... [...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 wel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
