Group Theory and Grammatical Description

This paper presents a model for linguistic description based on group theory. A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonolog-ical forms, and their inverses. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. We show applications of this model to parsing and generation, long-distance movement, and quan-tiier scoping. We believe that by moving from the free monoid over a vocabulary V | standard in formal language studies | to the free group over V, deep aanities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established could be considerable.