Generalized Discontinuity

  • Glyn Morrill
  • Oriol Valentín
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7395)


We define and study a calculus of discontinuity, a version of displacement calculus, which is a logic of segmented strings in exactly the same sense that the Lambek calculus is a logic of strings. Like the Lambek calculus, the displacement calculus is a sequence logic free of structural rules, and enjoys Cut-elimination and its corollaries: the subformula property, decidability, and the finite reading property. The foci of this paper are a formulation with a finite number of connectives, and consideration of how to extend the calculus with defined connectives while preserving its good properties.


Sequent Calculus Categorial Grammar Logical Syntax Logical Grammar Phrase Type 
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  1. 1.
    Bach, E.: Discontinuous constituents in generalized categorial grammars. In: Burke, V.A., Pustejovsky, J. (eds.) Proceedings of the 11th Annual Meeting of the North Eastern Linguistics Society, New York, pp. 1–12. GLSA Publications, Department of Linguistics, University of Massachussets at Amherst, Amherst, Massachussets (1981)Google Scholar
  2. 2.
    Bach, E.: Some Generalizations of Categorial Grammars. In: Landman, F., Veltman, F. (eds.) Varieties of Formal Semantics: Proceedings of the Fourth Amsterdam Colloquium, pp. 1–23. Foris, Dordrecht (1984); Reprinted in Savitch, W.J., Bach, E., Marsh, W., Safran-Naveh, G., (eds.) The Formal Complexity of Natural Language, pp. 251–279. D. Reidel, Dordrecht (1987)Google Scholar
  3. 3.
    Girard, J.-Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Lambek, J.: The mathematics of sentence structure. American Mathematical Monthly 65, 154–170 (1958); Reprinted in Buszkowski, W., Marciszewski, W., van Benthem, J., (eds.) Categorial Grammar. Linguistic & Literary Studies in Eastern Europe, vol. 25 153–172. John Benjamins, Amsterdam (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Lambek, J.: Deductive systems and categories, II: Standard constructions and closed categories. In: Hilton, P. (ed.) Category Theory, Homology Theory and Applications. Lecture Notes in Mathematics, vol. 86, pp. 76–122. Springer (1969)Google Scholar
  6. 6.
    Moortgat, M.: Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus. Foris, Dordrecht, PhD thesis. Universiteit van Amsterdam (1988)Google Scholar
  7. 7.
    Moortgat, M.: Symmetric categorial grammar. Journal of Philosophical Logic (2009)Google Scholar
  8. 8.
    Morrill, G.: Towards Generalised Discontinuity. In: Jäger, G., Monachesi, P., Penn, G., Wintner, S. (eds.) Proceedings of the 7th Conference on Formal Grammar, Trento, ESSLLI, pp. 103–111 (2002)Google Scholar
  9. 9.
    Morrill, G., Fadda, M., Valentín, O.: Nondeterministic Discontinuous Lambek Calculus. In: Geertzen, J., Thijsse, E., Bunt, H., Schiffrin, A. (eds.) Proceedings of the Seventh International Workshop on Computational Semantics, IWCS 2007, pp. 129–141. Tilburg University (2007)Google Scholar
  10. 10.
    Morrill, G., Merenciano, J.-M.: Generalising discontinuity. Traitement Automatique des Langues 37(2), 119–143 (1996)Google Scholar
  11. 11.
    Morrill, G., Valentín, O.: Displacement calculus. Linguistic Analysis (forthcoming)Google Scholar
  12. 12.
    Morrill, G., Valentín, O., Fadda, M.: Dutch Grammar and Processing: A Case Study in TLG. In: Bosch, P., Gabelaia, D., Lang, J. (eds.) TbiLLC 2007. LNCS (LNAI), vol. 5422, pp. 272–286. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Morrill, G., Valentín, O., Fadda, M.: The Displacement Calculus. Journal of Logic, Language and Information (forthcoming)Google Scholar
  14. 14.
    Morrill, G.V.: Categorial Grammar: Logical Syntax, Semantics, and Processing. Oxford University Press, Oxford (2010)Google Scholar
  15. 15.
    Pentus, M.: Lambek grammars are context-free. Technical report, Dept. Math. Logic, Steklov Math. Institute, Moskow (1992); Also published as ILLC Report, University of Amsterdam, 1993, and in Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science, Montreal (1993)Google Scholar
  16. 16.
    Shieber, S.: Evidence Against the Context-Freeness of Natural Language. Linguistics and Philosophy 8, 333–343 (1985); Reprinted in Savitch, W.J., Bach, E., Marsh, W., Safran-Naveh, G., (eds.) The Formal Complexity of Natural Language, pp. 320–334. D. Reidel, Dordrecht (1987) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Glyn Morrill
    • 1
  • Oriol Valentín
    • 2
  1. 1.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaSpain
  2. 2.Barcelona Media, Centre d’InnovacióUniversitat Pompeu FabraSpain

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