Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T22:46:16.725Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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