Phrase Structure Grammar

Abstract

Transformational grammars for natural languages, as currently envisaged, deploy a large number of devices: complex symbols, base rules, rule schemata, lexical insertion rules, lexical redundancy rules, movement rules, coindexing procedures, binding conventions, local and nonlocal filters, case marking conventions, feature percolation, constraints on movement, and so on. The mathematical properties of the resulting baroque systems are almost entirely unknown: we are ignorant, for example, as to whether ungrammaticality with respect to such grammars is decidable, i.e. given an arbitrary string on the terminal vocabulary, no way is known of proving that that string is not generated by the grammar. In this situation, claims by grammarians to the effect that such and such a string of words cannot be generated by their grammar merely reflect their intuitions about the apparatus they are using. These intuitions cannot be verified at present and may indeed by unverifiable in principle (i.e. if the class of grammars permitted under universal grammar generate nonrecursive sets).