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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 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 \Diamond Q ... [...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] |
Conditional Sentence
A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will be cancelled." They are so called because the impact of the sentence’s main clause is ''conditional'' on a subordinate clause. A full conditional thus contains two clauses: the subordinate clause, called the ''antecedent'' (or ''protasis'' or ''if-clause''), which expresses the condition, and the main clause, called the ''consequent'' (or ''apodosis'' or ''then-clause'') expressing the result. To form conditional sentences, languages use a variety of grammatical forms and constructions. The forms of verbs used in the antecedent and consequent are often subject to particular rules as regards their tense, aspect, and mood. Many languages have a specialized type of verb form called the conditional mood – broadly equivalent in meaning to the English "would (do something)" – for use in some types of conditional sentences. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability 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 Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to th ... [...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 t ... [...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] |
Sluicing
In syntax, sluicing is a type of 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. 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 why. (=why he doesn't like the lentils) ::Someone has eaten the soup. Unfortunately, I don't know who. (=who has eaten th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simplification Of Disjunctive Antecedents
In formal semantics (natural language), formal semantics and philosophical logic, simplification of disjunctive antecedents (SDA) is the phenomenon whereby a disjunction in the antecedent of a conditional sentence, conditional appears to distributive property, 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 validity (logic), 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 Counterfactual_conditional#Variably_strict_conditional, similarity analysis of counterfactuals. In these approaches, a counterfactual (A \lor B) > C is predicted to ... [...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 imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality, causation. For instance, in epistemic modal logic, the well-formed_formula, formula \Box P can be used to represent the statement that P is known. In deontic modal logic, that same formula can represent that P is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula \Box P \rightarrow P as a Tautology_(logic), tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operation, unary operators such as \Diamond and \Box, representing possibility and necessi ... [...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. Biography 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, Dav ... [...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] |
Deontic Logic
Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It can be used to formalize imperative logic, or directive modality in natural languages. Typically, a deontic logic uses ''OA'' to mean ''it is obligatory that A'' (or ''it ought to be (the case) that A''), and ''PA'' to mean ''it is permitted (or permissible) that A'', which is defined as PA\equiv \neg O\neg A. In natural language, the statement "You may go to the zoo OR the park" should be understood as Pz\land Pp instead of Pz\lor Pp, as both options are permitted by the statement. When there are multiple agents involved in the domain of discourse, the deontic modal operator can be specified to each agent to express their individual obligations and permissions. For example, by using a subscript O_i for agent a_i, O_iA means that "It i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
