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In mathematics, equivalent definitions are used in two somewhat different ways. First, within a particular mathematical theory (for example, Euclidean geometry ), a notion (for example, ellipse or minimal surface) may have more than one definition. These definitions are equivalent in the context of a given mathematical structure ( Euclidean ...
Syntax was recognized as the focal point of language production, in which a finite set of rules can produce an infinite number of sentences. Subsequently, morphology (i.e. the study of structure and formation of words) and phonology (i.e. the study of organization of sounds in languages) were relegated in importance.
In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. In other cases the dual of the dual – the double dual or bidual – is not ...
In linguistics, syntax (/ ˈ s ɪ n t æ k s / SIN-taks) [1] [2] is the study of how words and morphemes combine to form larger units such as phrases and sentences.Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency), [3] agreement, the nature of crosslinguistic variation, and the relationship between form and meaning ().
In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean -valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed ...
The propositional calculus[a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4][5] It deals with propositions [1] (which can be true or false) [6] and relations between propositions, [7] including the construction of ...
Linguistics. Lexical semantics (also known as lexicosemantics), as a subfield of linguistic semantics, is the study of word meanings. [1][2] It includes the study of how words structure their meaning, how they act in grammar and compositionality, [1] and the relationships between the distinct senses and uses of a word.
t. e. 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 ...