Grammar, Formal

Abstract

The term ‘grammar’, which traditionally designated a branch of linguistics, has acquired, since the time of the early works of Chomsky, a new meaning. It stands for an abstract object, viz. a system or a relational structure in the sense given to this term by model theory (q.v.). Such a system consists of the following constituents: (1) a set of individual objects called the universe of discourse — let it be denoted by U; (2) subsets of U, if there are any to be designated; (3) relations and/or functions, i.e. ordered pairs (or triples, quadruples etc.) whose members belong to U; (4) a distinguished (if necessary) element of U. In a grammar the set U consists of words, relations are grammatical rules and the distinguished element is a symbol, being the starting point (sometimes the end point, see §2.2.2) of syntactic derivations. A grammar construed as a system is a device to produce well-formed expressions of a language by means of grammatical rules operating on words or strings of words called expressions. The adjective ‘formal’, when applied to the term ‘grammar’, is to indicate formal approach in terms of set theory, algebra etc.