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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] |
Formal Semantics (natural Language)
Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. It provides accounts of what linguistic expressions mean and how their meanings are composed from the meanings of their parts. The enterprise of formal semantics can be thought of as that of reverse-engineering the semantic components of natural languages' grammars. Overview Formal semantics studies the denotations of natural language expressions. High-level concerns include compositionality, reference, and the nature of meaning. Key topic areas include scope, modality, binding, tense, and aspect. Semantics is distinct from pragmatics, which encompasses aspects of meaning which arise from interaction and communicative intent. Formal semantics is an interdisciplinary field, often viewed as a subfield of both linguistics and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 necessity operator from modal logic. For any two propositions ''p'' and ''q'', the formula ''p'' → ''q'' says that ''p'' materially implies ''q'' while \Box (p \rightarrow q) says that ''p'' strictly implies ''q''. Strict conditionals are the result of Clarence Irving Lewis's attempt to find a conditional for logic that can adequately express indicative conditionals in natural language. They have also been used in studying Molinist theology. Avoiding paradoxes The strict conditionals may avoid paradoxes of material implication. The following statement, for example, is not correctly formalized by material implication: : If Bill Gates has graduated in Medicine, then Elvis never died. This condition should clearly be false: the degree of Bi ... [...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] |
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] |
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] |
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] |
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] |
Subordination (linguistics)
In linguistics, subordination (abbreviated variously , , or ) is a principle of the hierarchical organization of linguistic units. While the principle is applicable in semantics, morphology, and phonology, most work in linguistics employs the term "subordination" in the context of syntax, and that is the context in which it is considered here. The syntactic units of sentences are often either subordinate or coordinate to each other. Hence an understanding of subordination is promoted by an understanding of coordination, and vice versa. Subordinate clauses Subordination as a concept of syntactic organization is associated closely with the distinction between ''coordinate'' and ''subordinate'' clauses. One clause is subordinate to another if it depends on it. The dependent clause is called a ''subordinate clause'' and the independent clause is called the ''main clause'' (= matrix clause). Subordinate clauses are usually introduced by subordinators (= subordinate conjunctions) such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Implicature
In pragmatics, a subdiscipline of linguistics, an implicature is something the speaker suggests or implies with an utterance, even though it is not literally expressed. Implicatures can aid in communicating more efficiently than by explicitly saying everything we want to communicate. The philosopher H. P. Grice coined the term in 1975. Grice distinguished ''conversational'' implicatures, which arise because speakers are expected to respect general rules of conversation, and ''conventional'' ones, which are tied to certain words such as "but" or "therefore". Take for example the following exchange: : A (to passer by): I am out of gas. : B: There is a gas station 'round the corner. Here, B does not say, but ''conversationally implicates'', that the gas station is open, because otherwise his utterance would not be relevant in the context. Conversational implicatures are classically seen as contrasting with entailments: They are not necessary or logical consequences of what is said, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Situation Semantics
In situation theory, situation semantics (pioneered by Jon Barwise and John Perry in the early 1980s) attempts to provide a solid theoretical foundation for reasoning about common-sense and real world situations, typically in the context of theoretical linguistics, theoretical philosophy, or applied natural language processing, Barwise and Perry Situations, unlike worlds, are not complete in the sense that every proposition or its negation holds in a world. According to ''Situations and Attitudes'', meaning is a relation between a discourse situation, a connective situation and a described situation. The original theory of ''Situations and Attitudes'' soon ran into foundational difficulties. A reformulation based on Peter Aczel's non-well-founded set theory was proposed by Barwise before this approach to the subject petered out in the early 1990s. HPSG Situation semantics is the first semantic theory that was used in head-driven phrase structure grammar (HPSG). Kratzer Bar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
