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Intersective Modifier
In linguistics, an intersective modifier is an expression which modifies another by delivering the intersection of their denotation In linguistics and philosophy, the denotation of a word or expression is its strictly literal meaning. For instance, the English word "warm" denotes the property of having high temperature. Denotation is contrasted with other aspects of meaning in ...s. One example is the English adjective "blue", whose intersectivity can be seen in the fact that being a "blue pig" entails being both blue and a pig. By contrast, the English adjective "former" is non-intersective since a "former president" is neither former nor a president. When a modifier is intersective, its contribution to the sentence's truth conditions do not depend on the particular expression it modifies. This means that one can test whether a modifier is intersective by seeing whether it gives rise to valid reasoning patterns such as the following. # Floyd is a Canadian surgeon. # Floyd is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Linguistics
Linguistics is the scientific study of language. The areas of linguistic analysis are syntax (rules governing the structure of sentences), semantics (meaning), Morphology (linguistics), morphology (structure of words), phonetics (speech sounds and equivalent gestures in sign languages), phonology (the abstract sound system of a particular language, and analogous systems of sign languages), and pragmatics (how the context of use contributes to meaning). Subdisciplines such as biolinguistics (the study of the biological variables and evolution of language) and psycholinguistics (the study of psychological factors in human language) bridge many of these divisions. Linguistics encompasses Outline of linguistics, many branches and subfields that span both theoretical and practical applications. Theoretical linguistics is concerned with understanding the universal grammar, universal and Philosophy of language#Nature of language, fundamental nature of language and developing a general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Grammatical Modifier
In linguistics, a modifier is an optional element in phrase structure or clause structure which ''modifies'' the meaning of another element in the structure. For instance, the adjective "red" acts as a modifier in the noun phrase "red ball", providing extra details about which particular ball is being referred to. Similarly, the adverb "quickly" acts as a modifier in the verb phrase "run quickly". Modification can be considered a high-level domain of the functions of language, on par with predication and reference. Premodifiers and postmodifiers Modifiers may come before or after the modified element (the ''head''), depending on the type of modifier and the rules of syntax for the language in question. A modifier placed before the head is called a premodifier; one placed after the head is called a postmodifier. For example, in ''land mines'', the word ''land'' is a premodifier of ''mines'', whereas in the phrase ''mines in wartime'', the phrase ''in wartime'' is a postmodifier of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Set Intersection
In set theory, the intersection of two sets A and B, denoted by A \cap B, is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A. Notation and terminology Intersection is written using the symbol "\cap" between the terms; that is, in infix notation. For example: \\cap\=\ \\cap\=\varnothing \Z\cap\N=\N \\cap\N=\ The intersection of more than two sets (generalized intersection) can be written as: \bigcap_^n A_i which is similar to capital-sigma notation. For an explanation of the symbols used in this article, refer to the table of mathematical symbols. Definition The intersection of two sets A and B, denoted by A \cap B, is the set of all objects that are members of both the sets A and B. In symbols: A \cap B = \. That is, x is an element of the intersection A \cap B if and only if x is both an element of A and an element of B. For example: * The intersection of the sets and is . * The number 9 is in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Denotation
In linguistics and philosophy, the denotation of a word or expression is its strictly literal meaning. For instance, the English word "warm" denotes the property of having high temperature. Denotation is contrasted with other aspects of meaning including '' connotation''. For instance, the word "warm" may evoke calmness, coziness, or kindness (as in the warmth of someone's personality) but these associations are not part of the word's denotation. Similarly, an expression's denotation is separate from pragmatic inferences it may trigger. For instance, describing something as "warm" often implicates that it is not hot, but this is once again not part of the word's denotation. Denotation plays a major role in several fields. Within semantics and philosophy of language, denotation is studied as an important aspect of meaning. In mathematics and computer science, assignments of denotations are assigned to expressions are a crucial step in defining interpreted formal languages. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Entailment
Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises?Beall, JC and Restall, Greg, Logical Consequence' The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.). All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth. Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. A sentence is said to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Validity (logic)
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be truth, true and the conclusion nevertheless to be False (logic), false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formula, well-formed formulas (also called ''wffs'' or simply ''formulas''). The validity of an argument can be tested, proved or disproved, and depends on its logical form. Arguments In logic, an argument is a set of related statements expressing the ''premises'' (which may consists of non-empirical evidence, empirical evidence or may contain some axiomatic truths) and a ''necessary conclusion based on the relationship of the premises.'' An argument is ''valid'' if and only if it would be contradicto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Deduction (logic)
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is ''sound'' if it is valid ''and'' all its premises are true. One approach defines deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning. Deductive logic studies under what conditions an argument is valid. According to the semantic approach, an argument is valid if th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Ambiguous
Ambiguity is the type of meaning in which a phrase, statement, or resolution is not explicitly defined, making for several interpretations; others describe it as a concept or statement that has no real reference. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement whose intended meaning cannot be definitively resolved, according to a rule or process with a finite number of steps. (The prefix '' ambi-'' reflects the idea of " two", as in "two meanings"). The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately obvious), whereas with vague information it is difficult to form any interpretation at the desired level of specificity. Linguistic forms Lexical ambiguity is contrasted with semantic ambiguity. The former represents a choice between a finite number of known and meaningful context-dependent interpretations. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Subsective Modifier
In linguistics, a subsective modifier is an expression which grammatical modifier, modifies another by delivering a subset of its denotation. For instance, the English adjective "skilled" is subsective since being a skilled surgeon entails being a surgeon. By contrast, the English adjective "alleged" is non-subsective since an "alleged spy" need not be an actual spy. # [\![ \text ]\!] \subseteq [\![\text]\!] A modifier can be subsective without being intersective modifier, intersective. For instance, calling someone an "old friend" entailment, entails that they are a friend but does not entail that they are elderly. The term "subsective" is most often applied to modifiers which are not intersective modifier, intersective and non-intersectivity is sometimes treated as part of its definition. There is no standard analysis for the formal semantics (natural language), semantics of (non-intersective) subsective modifiers. Early work such as Richard Montague, Montague (1970) took subsec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Compositionality
In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. The principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the principle has never been explicitly stated by Frege, and arguably it was already assumed by George Boole decades before Frege's work. The principle of compositionality (also known as semantic compositionalism) is highly debated in linguistics. Among its most challenging problems there are the issues of contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations. History Discussion of compositionality started to appear at the beginning of the 19th century, during which it was debated whether what was most fundamental in language was compositionalit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Type Theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations are: * Typed λ-calculus of Alonzo Church * Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Type Shifter
In formal semantics, a type shifter is an interpretation rule that changes an expression's semantic type. For instance, the English expression "John" might ordinarily denote John himself, but a type shifting rule called can raise its denotation to a function which takes a property and returns "true" if John himself has that property. Lift can be seen as mapping an individual onto the principal ultrafilter that it generates. # Without type shifting: \, \, ohn.html" ;"title="![John">![John!= j # Type shifting with : ohn.html" ;"title="![John">![John!= \lambda P_ . P(j) Type shifters were proposed by Barbara Partee and Mats Rooth in 1983 to allow for systematic type ambiguity. Work of the period assumed that syntactic category, syntactic categories corresponded directly with semantic types, and researchers thus had to "generalize to the worst case" when particular uses of particular expressions from a given category required an especially high type. Moreover, Partee argued ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |