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Product-free Lambek calculus and context-free grammars

Published online by Cambridge University Press:  12 March 2014

Mati Pentus
Mati Pentus*
Affiliation:
Department of Mathematical Logic, Faculty of Mechanics and Mathematics, Moscow University, 119899, Moscow, Russia, E-mail: pentus@lpcs.math.msu.ru
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Abstract

In this paper we prove the Chomsky Conjecture (all languages recognized by the Lambek calculus are context-free) for both the full Lambek calculus and its product-free fragment. For the latter case we present a construction of context-free grammars involving only product-free types.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 2 , June 1997 , pp. 648 - 660
Copyright
Copyright © Association for Symbolic Logic 1997

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References

REFERENCES

[1] Bar-Hillel, Y., Gaifman, C., and Shamir, E., On categorial and phrase-structure grammars, Bull. Res. Council Israel Sect. F, vol. 9F (1960), pp. 1–16.Google Scholar
[2] Buszkowski, W., The equivalence of unidirectional Lambek categorial grammars and context-free grammars, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 31 (1985), pp. 369–384.CrossRefGoogle Scholar
[3] Buszkowski, W., Generative power of categorial grammars, Categorial grammars and natural language structures (Oehrle, R. T., Bach, E., and Wheeler, D., editors), Reidel, Dordrecht, 1988, pp. 69–94.CrossRefGoogle Scholar
[4] Buszkowski, W., On generative capacity of the Lambek calculus, Logics in AI (van Eijck, J., editor), Springer-Verlag, Berlin, 1991, pp. 139–152.CrossRefGoogle Scholar
[5] Buszkowski, W., On the equivalence of Lambek categorial grammars and basic categorial grammars, ILLC Prepublication Series, vol. LP–93–07, Institute for Logic, Language and Computation, University of Amsterdam, 1993.Google Scholar
[6] Chomsky, N., Formal properties of grammars, Handbook of mathematical psychology (Luce, R. D.et al., editors), vol. 2, Wiley, New York, 1963, pp. 323–418.Google Scholar
[7] Cohen, J.M., The equivalence of two concepts of categorial grammar, Information and Control, vol. 10 (1967), pp. 475–484.CrossRefGoogle Scholar
[8] Lambek, J., The mathematics of sentence structure, American Mathematical Monthly, vol. 65 (1958), no. 3, pp. 154–170.CrossRefGoogle Scholar
[9] Pentus, M., Equivalent types in Lambek calculus and linear logic, Series Logic and Computer Science, Department of Math. Logic, Steklov Math. Institute, Moscow, 1992, preprint no. 2.Google Scholar
[10] Pentus, M., Lambek grammars are context free, Series Logic and Computer Science, Department of Math. Logic, Steklov Math. Institute, Moscow, 1992, preprint no.8.Google Scholar
[11] Pentus, M., Lambek grammars are context free, Proceedings of the 8th annual IEEE symposium on logic in computer science, LICS '93, 1993, pp. 429–433.Google Scholar
[12] Roorda, D., Resource logics: Proof-theoretical investigations, Ph.D. thesis, Fac. Math, and Comp. Sc., University of Amsterdam, 1991.Google Scholar
[13] van Benthem, J., Language in action, North-Holland, Amsterdam, 1991.Google Scholar