Formal Language

formal language

[¦fȯr·məl ′laŋ·gwij] (computer science) An abstract mathematical object used to model the syntax of a programming or natural language.

Formal Language

(1) In a broad sense, a formal language is a set of in some way specialized linguistic means that is provided with more or less precisely defined rules for forming expressions (the syntax of the formal language) and for assigning meaning to the expressions (the semantics of the language). Generally speaking, this use of the term “formal language” does not assume any special restrictions on the syntactic structure, semantic rules, or purpose of the language. For example, the expressions “H₂O,” voda, eau, “water,” Wasser, and vesi can, in principle, be considered in equal measure elements of the formal language of chemistry.

(2) In logic, a formal, or formalized, language is an interpreted calculus, that is, a formal system with an interpretation. The use of formal languages is characteristic of mathematical logic, which is often defined as “the subject of formal logic as studied through the construction of formal languages.” It should, however, be noted that this definition is by no means an inherent attribute of presentations of mathematical logic. The concept of formal language not only does not generally occur in particular logico-mathematical languages but, strictly speaking, is not even an element of any specific metalanguages. It is, rather, a useful working term in preliminary heuristic elucidations of the subject matter of mathematical logic.

REFERENCE

Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. Introduction (subsecs. 00–09). Translated from English.

单词	formal language
释义	formal language formal language n 1. (Logic) a language designed for use in situations in which natural language is unsuitable, as for example in mathematics, logic, or computer programming. The symbols and formulas of such languages stand in precisely specified syntactic and semantic relations to one another 2. (Logic) logic a logistic system for which an interpretation is provided: distinguished from formal calculus in that the semantics enable it to be regarded as about some subject matter Translations Formal Language formal language [¦fȯr·məl ′laŋ·gwij] (computer science) An abstract mathematical object used to model the syntax of a programming or natural language. Formal Language (1) In a broad sense, a formal language is a set of in some way specialized linguistic means that is provided with more or less precisely defined rules for forming expressions (the syntax of the formal language) and for assigning meaning to the expressions (the semantics of the language). Generally speaking, this use of the term “formal language” does not assume any special restrictions on the syntactic structure, semantic rules, or purpose of the language. For example, the expressions “H₂O,” voda, eau, “water,” Wasser, and vesi can, in principle, be considered in equal measure elements of the formal language of chemistry. (2) In logic, a formal, or formalized, language is an interpreted calculus, that is, a formal system with an interpretation. The use of formal languages is characteristic of mathematical logic, which is often defined as “the subject of formal logic as studied through the construction of formal languages.” It should, however, be noted that this definition is by no means an inherent attribute of presentations of mathematical logic. The concept of formal language not only does not generally occur in particular logico-mathematical languages but, strictly speaking, is not even an element of any specific metalanguages. It is, rather, a useful working term in preliminary heuristic elucidations of the subject matter of mathematical logic. REFERENCE Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. Introduction (subsecs. 00–09). Translated from English.
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