# Strong completeness of the Lambek Calculus with respect to Relational Semantics

Banach Center Publications (1993)

- Volume: 28, Issue: 1, page 209-217
- ISSN: 0137-6934

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topMikulás, Szabolcs. "Strong completeness of the Lambek Calculus with respect to Relational Semantics." Banach Center Publications 28.1 (1993): 209-217. <http://eudml.org/doc/262731>.

@article{Mikulás1993,

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.},

author = {Mikulás, Szabolcs},

journal = {Banach Center Publications},

keywords = {relational semantics; Lambek calculus; strong completeness theorems},

language = {eng},

number = {1},

pages = {209-217},

title = {Strong completeness of the Lambek Calculus with respect to Relational Semantics},

url = {http://eudml.org/doc/262731},

volume = {28},

year = {1993},

}

TY - JOUR

AU - Mikulás, Szabolcs

TI - Strong completeness of the Lambek Calculus with respect to Relational Semantics

JO - Banach Center Publications

PY - 1993

VL - 28

IS - 1

SP - 209

EP - 217

AB - 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.

LA - eng

KW - relational semantics; Lambek calculus; strong completeness theorems

UR - http://eudml.org/doc/262731

ER -

## References

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- [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.
- [vB91] J. .van Benthem, Language in Action, North-Holland, 1991. Zbl0743.03018
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- [Go87] R. Goldblatt, Logics of Time and Computation, CSLI Lecture Notes 7, Stanford Univ., 1987.
- [La58] J. Lambek, The mathematics of sentence structure, Amer. Math. Monthly 65 (1958), 154-170. Zbl0080.00702
- [Mi91] Sz. Mikulás, The completeness of the Lambek Calculus w.r.t. Relational Semantics, lecture at the Banach Center, Warsaw, 17th October, 1991.
- [Né91] I. Németi, Algebraizations of quantifier logics, an introductory overview, Studia Logica 50 (3/4) (1991), 485-570.
- [Ro91] D. Roorda, Resource Logics: Proof-theoretical Investigations, Ph.D. thesis, Fac. Math. and Comput. Sci., Univ. of Amsterdam, 1991.
- [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. Zbl0793.03076

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