![]() Johnson, D., 1997, Presentations of Groups, Cambridge: Cambridge University Press. Girard, J., 1987, “Linear logic,” Theoretical Computer Science 50(1), 1–102. 348–352 in Proceedings of the Coling-ACL Conference, Montreal: ACL. Strzalkowski, ed., Dordrecht: Kluwer Academic Publishers.ĭymetman, M.: 1998, “Group theory and linguistic processing,” pp. ![]() 33–57 in Reversible Grammar in Natural Language Processing, T. 909, Berlin: Springer-Verlag.Ĭolmerauer, A., 1970, “Les systèmes-Q ou un formalisme pour analyser et synthétiser des phrases sur ordinateur,” Publication interne 43, Département d'Informatique, Université de Montréal, Montréal.ĭalrymple, M., Lamping, J., Pereira, F., and Saraswat, V., 1995, “Linear logic for meaning assembly,” in Proceedings of the Workshop on Computational Logic for Natural Language Processing, Edinburgh.ĭymetman, M., 1992, “Transformations de grammaires logiques et réversibilité en traduction automatique,” Thèse d'État, Université Joseph Fourier (Grenoble 1), Grenoble, France.ĭymetman, M., 1994, “Inherently reversible grammars,” pp. The paper argues that by moving from the free monoid over a vocabulary V (standard in formal language theory) 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 can be considerable.Ībrusci, V., 1991, “Phase semantics and sequent calculus for pure non-commutative classical linear logic,” Journal of Symbolic Logic 56(4), 1403–1451.Ĭhenadec, P.L., 1995, “A survey of symmetrized and complete group presentations,” pp. We give examples showing the value of conjugacy for handling long-distance movement and quantifier scoping both in parsing and generation. ![]() We show how the G-grammar can be “oriented” for each of the modes by reformulating the lexical expressions as rewriting rules adapted to parsing or generation, which then have strong decidability properties (inherent reversibility). A G-grammar provides a symmetrical specification of the relation between a logical form and a phonological string that is neutral between parsing and generation modes. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. ![]() A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonological forms, and inverses of those. This paper presents such a model, and demonstrates the connection between linguistic processing and the classical algebraic notions of non-commutative free group, conjugacy, and group presentations. Some connections between the Lambek calculus and computations in groups have long been known (van Benthem, 1986) but no serious attempt has been made to base a theory of linguistic processing solely on group structure. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995 Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties.
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