Group Theory and Computational Linguistics

• Authors: Marc Dymetman
• Venue: Journal of Logic, Language and Information
• Year: 1998

There is currently much interest in bringing together the traditionof categorial grammar, and especially the Lambek calculus, with therecent paradigm of linear logic to which it has strong ties. Oneactive research area is designing non-commutative versions of linearlogic (Abrusci, 1995; Retoré, 1993) which can be sensitive to wordorder while retaining the hypothetical reasoning capabilities ofstandard (commutative) linear logic (Dalrymple et al., 1995). Someconnections between the Lambek calculus and computations in groupshave long been known (van Benthem, 1986) but no serious attempt hasbeen made to base a theory of linguistic processing solely on groupstructure. This paper presents such a model, and demonstrates theconnection between linguistic processing and the classical algebraicnotions of non-commutative free group, conjugacy, andgroup presentations. A grammar in this model, or G-grammar is a collection of lexical expressions which areproducts of logical forms, phonological forms, and inverses ofthose. Phrasal descriptions are obtained by forming products oflexical expressions and by cancelling contiguous elements which areinverses of each other. A G-grammar provides a symmetricalspecification of the relation between a logical form and aphonological string that is neutral between parsing and generationmodes. We show how the G-grammar can be ’’oriented‘‘ for each of themodes by reformulating the lexical expressions as rewriting rulesadapted to parsing or generation, which then have strongdecidability properties (inherent reversibility). We give examplesshowing the value of conjugacy for handling long-distance movementand quantifier scoping both in parsing and generation. The paperargues that by moving from the free monoid over a vocabulary V(standard in formal language theory) to the free group over V, deepaffinities between linguistic phenomena and classical algebra cometo the surface, and that the consequences of tapping themathematical connections thus established can be considerable.