1998/05/07 by Marc Dymetman, Dymetman, Marc
Computer Science · #Computation and Language (cs.CL) #FOS: Computer and information sciences #Logic, programming, and type systems #Natural Language Processing Techniques #cmp-lg #cs.CL #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.cmp-lg/9805002
17 pages (Latex, Postscript). A shorter version of this paper will appear in the Coling/ACL 98 Proceedings. See http://www.xrce.xerox.com/people/dymetman/dymetman.html
arxiv created 1998/05/07 · openalex publication_date 1998/05/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, phonological 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 quantifier 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 affinities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established could be considerable.