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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 scientific study of linguistic meaning through formal tools from logic and mathematics. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. Formal semanticists rely on diverse methods to analyze natural language. Many examine the meaning of a sentence by studying the circumstances in which it would be true. They describe these circumstances using abstract mathematical models to represent entities and their features. The principle of compositionality helps them link the meaning of expressions to abstract objects in these models. This principle asserts that the meaning of a compound expression is determined by the meanings of its parts. Propositional and predicate logic are formal systems used to analyze the semantic structure of sentences. They introduce concepts like singular terms, predicates, quantifiers, and logical connectives to represent the logical form of natural language expres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjective
An adjective (abbreviations, abbreviated ) is a word that describes or defines a noun or noun phrase. Its semantic role is to change information given by the noun. Traditionally, adjectives are considered one of the main part of speech, parts of speech of the English language, although historically they were classed together with Noun, nouns. Nowadays, certain words that usually had been classified as adjectives, including ''the'', ''this'', ''my'', etc., typically are classed separately, as Determiner (class), determiners. Examples: * That's a ''funny'' idea. (Prepositive attributive) * That idea is ''funny''. (Predicate (grammar), Predicative) * * The ''good'', the ''bad'', and the ''funny''. (Substantive adjective, Substantive) * Clara Oswald, completely ''fictional'', died three times. (Apposition, Appositive) Etymology ''Adjective'' comes from Latin ', a calque of (whence also English ''epithet''). In the grammatical tradition of Latin and Greek, because adjectives were I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinality
The thumb is the first digit of the hand, next to the index finger. When a person is standing in the medical anatomical position (where the palm is facing to the front), the thumb is the outermost digit. The Medical Latin English noun for thumb is ''pollex'' (compare ''hallux'' for big toe), and the corresponding adjective for thumb is ''pollical''. Definition Thumb and fingers The English word ''finger'' has two senses, even in the context of appendages of a single typical human hand: 1) Any of the five terminal members of the hand. 2) Any of the four terminal members of the hand, other than the thumb. Linguistically, it appears that the original sense was the first of these two: (also rendered as ) was, in the inferred Proto-Indo-European language, a suffixed form of (or ), which has given rise to many Indo-European-family words (tens of them defined in English dictionaries) that involve, or stem from, concepts of fiveness. The thumb shares the following with each of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negative Polarity Item
In grammar and 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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection (set Theory)
In set theory, the intersection of two Set (mathematics), 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 n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Downward Entailing
In linguistics, 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, 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" entailment (pragmatics), 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-en ... [...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 it is either entirely non-decreasing, or entirely non-increasing. 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 termed ''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\right), so i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Upward Entailing
Upward may refer to: Arts * ''Upward'' (Kandinsky), a 1929 painting by Russian abstract painter Wassily Kandinsky * ''Upwards'' (album), a 2003 album British rapper Ty Organizations * Upward Bound Upward Bound is a federally funded educational program within the United States. The program is one of a cluster of programs now referred to as Federal TRIO Programs, TRiO, all of which owe their existence to the federal Economic Opportunity Act ..., a federally funded educational program within the United States * Upward Bound High School, a school in Hartwick, New York 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 See also * * * up (other) {{Disambi ... [...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 it is either entirely non-decreasing, or entirely non-increasing. 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 termed ''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\right), so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determiner (linguistics)
Determiner, also called determinative ( abbreviated ), is a term used in some models of grammatical description to describe a word or affix belonging to a class of noun modifiers. A determiner combines with a noun to express its reference. Examples in English include articles (''the'' and ''a''/''an''), demonstratives (''this'', ''that''), possessive determiners (''my,'' ''their''), and quantifiers (''many'', ''both''). Not all languages have determiners, and not all systems of grammatical description recognize them as a distinct category. Description The linguistics term "determiner" was coined by Leonard Bloomfield in 1933. Bloomfield observed that in English, nouns often require a qualifying word such as an article or adjective. He proposed that such words belong to a distinct class which he called "determiners". If a language is said to have determiners, any articles are normally included in the class. Other types of words often regarded as belonging to the determiner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
