Conjoinability in Pregroups

• Autorzy: Kiślak-Malinowska A.
• Języki publikacji: EN

Abstrakty

EN

Pregroups are introduced by Lambek as a framework for syntactic analysis of Natural Language; they are algebraic models of Compact Bilinear Logic. In the present paper we consider the problem of conjoinability in the calculus of pregroups. We show that two types are conjoinable in a pregroup iff they are equal in a free group. This result is analogous to Pentus' characterization of conjoinability in the Lambek calculus.

Słowa kluczowe

EN

pregroups; group theory; abelian groups; amalgam; natural language processing

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2004
• Tom: Vol. 61, nr 1
• Strony: 29--36
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Kiślak-Malinowska A.

• Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland,

Bibliografia

• [1] Abrusci, V. M., Casadio C. (eds.). New Perspectives in Logic and Formal Linguistics, ISBN 88-8319-747-8, Bulzoni Editore, Roma, 2002.
• [2] Buszkowski W., Lambek grammars based on pregroups, in; Logical Aspects of Computational Linguistics (P. de Groote, G. Morril and C. Retore, Eds.), Proc. LACL'0l, LNAI2099, Springer, Berlin, 2001,95-109.
• [3] Buszkowski W., Cut elimination for the Lambek calculus of adjoints, in [1], 85-94.
• [4] Buszkowski W., Sequent systems for compact bilinear logic. Mathematical Logic Quarterly 49, No.5, 2003, 467-474.
• [5] Foret A., On mixing deduction and substitution in Lambek categorial grammars, in: Logical Aspects of Computational Linguistics (P de Groote, G. Morril and C. Retore, Eds.), Proc. LACL'0l, LNAI 2099, Springer, Berlin, 2001.
• [6] Kislak A., Pregroups versus English and Polish grammar, in [1], 129-154.
• [7] Lambek J., The mathematics of sentence structure. The American Mathematical Monthly 65, (1958), 154-170.
• [8] Lambek J., Type grammars revisited, in: Logical Aspects of Computational Linguistics (A. Lecomte, F. Lamarche and G. Perrier, Eds.), LNAI 1582, Springer, Berlin, 1999, 1-27.
• [9] Lambek J., Type Grammars as Pregroups, Grammars 4 (2001), 21-39.
• [10] Lambek J., Pregroups: a new algebraic approach to sentence structure, in [1], 39-54.
• [11] Pentus M., The conjoinability relation in Lambek calculus and linear logic, ILLC Prepublications Series ML-93-03, Institute for Logic, Language and Computation, University of Amsterdam, 1993