Formal Grammar

Grammar, Formal 

in linguistics, a logical system or calculation that poses a certain set of (“grammatical”) chains (finite sequences) constructed from symbols of a given finite set called an alphabet or basic (terminal) vocabulary.

In the theory of formal grammar, these chains are interpreted as linguistic objects of various levels (for example, syllables [chains of phones], word forms [chains of morphs], and sentences [chains of word forms]). Introduced into linguistics by the American scholar N. Chomsky, formal grammar represents a means for the strict description of natural languages. Formal grammar theory constitutes an important section of mathematical linguistics, which in turn is subdivided into generative grammar and recognition grammar.

Generative grammar poses a set of (grammatical) chains through the enumeration of the chains together with statements about their structure. Generative grammar can construct any grammatical chain, supplying it with a characteristic of its structure; it must not construct even a single incorrect chain. The best known of the generative grammars are the so-called Chomskian grammars.

Recognition grammar offers a set of (grammatical) chains as a result of their recognition: for any chain produced, the grammar decides whether or not it is grammatical; in the case of an affirmative answer, the grammar makes statements about the structure of the chain. The best known of the recognition grammars are the categorial grammars introduced by K. Ajdukiewicz and Y. Bar-Hillel.

REFERENCES

Chomsky, N., and G. Miller. “Vvedenie v formal’nyi analiz est-estvennykh iazykov.” In Kiberneticheskii sbornik, Novaia seriia. vol. 1. Moscow. 1965.
Chomsky, N. “Formal’nye svoistva grammatik.” In Kiberneticheskii sbornik, Novaia seriia, vol. 2. Moscow, 1966.
Bar-Hillel. Y. “Nekotorye novye resul’taty v teoreticheskoi lingvi-stike.” In Matematicheskaia logika i ee primenenie. Moscow, 1965.
Lambek, J. “Matematicheskoe issledovanie struktury predlo-zhenii.” In Matematicheskaia lingvistika. Moscow. 1964.
Gladkii, A. V. Lektsii po matematicheskoi lingvistike dlia studentov NGU. Novosibirsk, 1966.
Gladkii, A. V., and I. A. Mel’chuk. Elementy matematicheskoi lingvistiki. Moscow. 1969. Pages 23–136.

I. A. MEL’CHUK