Journal of Logic, Language and Information

, Volume 13, Issue 1, pp 47–59 | Cite as

Residuation, Structural Rules and Context Freeness

  • Gerhard Jäger

Abstract

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

categorial grammar generative capacity mathematical linguistics multimodal type logical grammar 

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References

  1. Bar-Hillel, Y., 1953, “A quasi-arithmetical notation for syntactic description, ” Language 29 (1953), 47-58.Google Scholar
  2. Bar-Hillel, Y., Gaifman, C., and Shamir, E., 1960, 'On categorial and phrase structure grammars', Bulletin of the Research Council of Israel F(9), 1-16.Google Scholar
  3. Buszkowski, W., 1986, “Generative capacity of nonassociative Lambek calculus, ” Bulletin of the Polish Academy of Sciences: Mathematics 34, 507-518.Google Scholar
  4. Carpenter, B., 1999, “The Turing-completeness of multimodal categorial grammars, ” Papers presented to Johan van Benthem in honor of his 50th birthday, European Summer School in Logic, Language and Information, Utrecht.Google Scholar
  5. Chomsky, N., 1957, Syntactic Structures, The Hague: Mouton.Google Scholar
  6. Cohen, J.M., 1967, “The equivalence of two concepts of categorial grammar, ” Information and Control 10, 475-484.Google Scholar
  7. Jäger, G., 2001, “On the generative capacity of multimodal categorial grammars, ” Journal of Language and Computation, to appear.Google Scholar
  8. Kandulski, M., 1988, “The equivalence of nonassociative Lambek categorial grammars and context free grammars, ” Zeitschrift fürMathematische Logik und Grundlagen der Mathematik 34, 41-52.Google Scholar
  9. Kandulski, M., 1995, “On commutative and nonassociative syntactic calculi and categorial grammars, ” Mathematical Logic Quarterly 65, 217-235.Google Scholar
  10. Kandulski, M., 1997, “On generalized Ajdukiewicz and Lambek calculi and grammars, ” Fundamenta Informaticae 30, 169-181.Google Scholar
  11. Lambek, J., 1958, “The mathematics of sentence structure, ” American Mathematical Monthly 65, 154-170.Google Scholar
  12. Lambek, J., 1961, “On the calculus of syntactic types, ” pp. 166-178 in Structure of Language and Its Mathematical Aspects, R. Jakobson, ed., Providence, RI: American Mathematical Society.Google Scholar
  13. Moortgat, M., 1988, Categorial Investigations. Logical and Linguistic Aspects of the Lambek Calculus, Dordrecht: Foris.Google Scholar
  14. Moortgat, M., 1996, “Multimodal linguistic inference, ” Journal of Logic, Language and Information 5, 349-385.Google Scholar
  15. Morrill, G., 1990, “Intensionality and Boundedness, ” Linguistics and Philosophy 13, 699-726.Google Scholar
  16. Pentus, M., 1993, “Lambek grammars are context-free, ” pp. 429-433 in Proceedings of the 8th Annual IEEE Symposium on Logic in Computer Science, New York: IEEE.Google Scholar
  17. Roorda, D., 1991, “Resource logics: Proof-theoretical investigations, ” Ph.D. Thesis, University of Amsterdam.Google Scholar
  18. Shieber, S., 1985, “Evidence against the context-freeness of natural language, ” Linguistics and Philosophy 8, 333-343.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Gerhard Jäger
    • 1
  1. 1.University of PotsdamPotsdamGermany

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