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Quantifiers (linguistics)
In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases. For example, the generalized quantifier ''every boy'' denotes the set of sets of which every boy is a member: \ This treatment of quantifiers has been essential in achieving a compositional semantics for sentences containing quantifiers. Type theory A version of type theory is often used to make the semantics of different kinds of expressions explicit. The standard construction defines the set of types recursively as follows: #''e'' and ''t'' are types. #If ''a'' and ''b'' are both types, then so is \langle a,b\rangle #Nothing is a type, except what can be constructed on the basis of lines 1 and 2 above. Given this definition, we have the simple types ''e'' and ''t'', but also a countable infinity of complex types, some of which include: \langle e,t\rangle;\qquad \langle t,t\rangle;\qquad \langle\langle e,t\rangle ... [...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] |
Adjective
In linguistics, an adjective (abbreviated ) is a word that generally modifies a noun or noun phrase or describes its referent. Its semantic role is to change information given by the noun. Traditionally, adjectives were considered one of the main parts of speech of the English language, although historically they were classed together with nouns. Nowadays, certain words that usually had been classified as adjectives, including ''the'', ''this'', ''my'', etc., typically are classed separately, as determiners. Here are some examples: * That's a funny idea. ( attributive) * That idea is funny. ( predicative) * * The good, the bad, and the funny. ( substantive) Etymology ''Adjective'' comes from Latin ', a calque of grc, ἐπίθετον ὄνομα, epítheton ónoma, additional noun (whence also English '' epithet''). In the grammatical tradition of Latin and Greek, because adjectives were inflected for gender, number, and case like nouns (a process called declension), th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinality
In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = \ contains 3 elements, and therefore A has a cardinality of 3. Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them. There are two approaches to cardinality: one which compares sets directly using bijections and injections, and another which uses cardinal numbers. The cardinality of a set is also called its size, when no confusion with other notions of size is possible. The cardinality of a set A is usually denoted , A, , with a vertical bar on each side; this is the same notation as absolute value, and the meaning depends on context. The cardinality of a set A may alternatively be denoted by n(A), , \operatorname(A), or \#A. History A crude sense of cardinality, an awareness that groups of things or events compare with other grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negative Polarity Item
In linguistics, a polarity item is a lexical item that is associated with affirmation or negation. An affirmation is a positive polarity item, abbreviated PPI or AFF. A negation is a negative polarity item, abbreviated NPI or NEG. The linguistic environment in which a polarity item appears is a licensing context. In the simplest case, an affirmative statement provides a licensing context for a PPI, while negation provides a licensing context for an NPI. However, there are many complications, and not all polarity items of a particular type have the same licensing contexts. In English As examples of polarity items, consider the English lexical items ''somewhat'' and ''at all'', as used in the following sentences: # I liked the film somewhat. # I didn't like the film at all. # *I liked the film at all. # *I didn't like the film somewhat. As can be seen, ''somewhat'' is licensed by the affirmative environment of sentence (1), but it is forbidden (anti-licensed) by the negative envi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection (set Theory)
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Downward Entailing
In linguistic semantics, a downward entailing (DE) propositional operator is one that constrains the meaning of an expression to a lower number or degree than would be possible without the expression. For example, "not," "nobody," "few people," "at most two boys." Conversely, an upward-entailing operator constrains the meaning of an expression to a higher number or degree, for example "more than one." A context that is neither downward nor upward entailing is ''non-monotone'', such as "exactly five." A downward-entailing operator reverses the relation of ''semantic strength'' among expressions. An expression like "run fast" is semantically ''stronger'' than the expression "run" since "John ran fast" entails "John ran," but not conversely. But a downward-entailing context reverses this strength; for example, the proposition "At most two boys ran" entails that "At most two boys ran fast" but not the other way around. An upward-entailing operator preserves the relation of semantic st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotone Decreasing
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entailment
Logical consequence (also entailment) 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 be a logical conse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upward Entailing
Upward may refer to: Music * ''Upwards'' (album), a 2003 album British hip-hop artist Ty Organizations * Upward Bound, a federally funded educational program within the United States * Upward Bound High School, a school in Hartwick, New York * Upwardly Global, an American non-profit organization People * Allen Upward (1863–1926), British poet, lawyer, politician and teacher * Christopher Upward (1938–2002), British orthographer, son of Edward Upward * Edward Upward (1903–2009), British novelist and short-story writer, cousin of Allen Upward Science * Upward (military project), the code name for assistance given to NASA during Project Apollo * upward continuation, a method used in oil exploration and geophysics * upward looking sonar, a sonar device * upward spiral Upward Spiral is a term used by Paul Kennedy in his book ''The Rise and Fall of Great Powers'' to describe the continually rising cost of military equipment relative to civilian manufactured goods. According t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotone Increasing
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determiner (linguistics)
A determiner, also called determinative (abbreviated ), is a word, phrase, or affix that occurs together with a noun or noun phrase and generally serves to express the reference of that noun or noun phrase in the context. That is, a determiner may indicate whether the noun is referring to a definite or indefinite element of a class, to a closer or more distant element, to an element belonging to a specified person or thing, to a particular number or quantity, etc. Common kinds of determiners include definite and indefinite articles (''the'', ''a''), demonstratives (''this'', ''that''), possessive determiners (''my,'' ''their''), cardinal numerals (''one'', ''two''), quantifiers (''many'', ''both''), distributive determiners (''each'', ''every''), and interrogative determiners (''which'', ''what''). Description Most determiners have been traditionally classed either as adjectives or pronouns, and this still occurs in traditional grammars: for example, demonstrative and poss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
