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ArticleOriginal scientific text

Title

Strong completeness of the Lambek Calculus with respect to Relational Semantics

Authors 1

Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Pf. 127, H-1364, Hungary

Abstract

In [vB88], Johan van Benthem introduces Relational Semantics (RelSem for short), and states Soundness Theorem for Lambek Calculus (LC) w.r.t. RelSem. After doing this, he writes: "it would be very interesting to have the converse too", i.e., to have Completeness Theorem. The same question is in [vB91, p. 235]. In the following, we state Strong Completeness Theorems for different versions of LC.

Bibliography

  1. [An88] H. Andréka, On the representation problem of distributive semilattice-ordered semigroups, preprint, Budapest 1988.
  2. [An91] H. Andréka, Representations of distributive lattice-ordered semigroups with binary relations, Algebra Universalis 28 (1991), 12-25.
  3. [ANS91] H. Andréka, I. Németi and I. Sain, On the strength of temporal proofs, Theoret. Comput. Sci. 80 (1991), 125-151.
  4. [vB88] J. .van Benthem, Semantic parallels in natural language and computation, Institute for Language, Logic and Information, Univ. of Amsterdam, 1988; also appeared in: H.-D. Ebbinghaus et al. (eds.), Logic Colloquium (Granada 1987), North-Holland, 1989, 331-375.
  5. [vB91] J. .van Benthem, Language in Action, North-Holland, 1991.
  6. [Do90] K. Došen, A brief survey of frames for the Lambek calculus, Z. Math. Logik Grundlag. Math. 38 (1992), 179-187.
  7. [Go87] R. Goldblatt, Logics of Time and Computation, CSLI Lecture Notes 7, Stanford Univ., 1987.
  8. [La58] J. Lambek, The mathematics of sentence structure, Amer. Math. Monthly 65 (1958), 154-170.
  9. [Mi91] Sz. Mikulás, The completeness of the Lambek Calculus w.r.t. Relational Semantics, lecture at the Banach Center, Warsaw, 17th October, 1991.
  10. [Né91] I. Németi, Algebraizations of quantifier logics, an introductory overview, Studia Logica 50 (3/4) (1991), 485-570.
  11. [Ro91] D. Roorda, Resource Logics: Proof-theoretical Investigations, Ph.D. thesis, Fac. Math. and Comput. Sci., Univ. of Amsterdam, 1991.
  12. [Sa90] I. Sain, Beth's and Craig's properties via epimorphisms and amalgamation in algebraic logic, in: C. H. Bergman, R. D. Maddux and D. L. Pigozzi (eds.), Algebraic Logic and Universal Algebra in Computer Science, Lecture Notes in Comput. Sci. 425, Springer, 1990, 209-226.
Banach Center Publications
1993/28/1
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Pages:
209-217
Main language of publication
English
Published
1993
Exact and natural sciences