On the Representation of Generative Grammars as First-Order Theories

Abstract

As is well known, a generative grammar is considered by Chomsky as a set of rules that, in particular, generates the sentences of a language. In this paper I shall try to make it plausible that for each such generative rule system a corresponding first-order theory can be effectively constructed such that, roughly speaking, what can be generated by the grammar, can be logically derived within this theory. A grammar represented as a first-order theory will provide thus, above all, a deductive nomological explanation of the sentences of a language in the sense of theory of knowledge (Wang, 1971b). We shall treat at first the problem of representation of the well-defined context-free grammar and then that of the less formalized transformational grammar.