Journal of Logic, Language and Information

, Volume 8, Issue 1, pp 45–81

A Resource Sensitive Interpretation of Lexical Functional Grammar

Article

Abstract

This paper investigates whether the fundamental linguistic insights and intuitions of Lexical Functional Grammar (LFG), which is usually presented as a “constraint-based” linguistic theory, can be reformulated in a “resource sensitive” framework using a substructural modal logic. In the approach investigated here, LFG's f-descriptions are replaced with expressions from a multi-modal propositional logic (with permutation and possibly limited contraction). In effect, the feature structure “unification” basis of LFG's f-structures is replaced with a very different resource based mechanism. It turns out that some linguistic analyses that required non-monotonic devices in LFG (such as the “constraint equations” in the Andrews (1982) analysis of Icelandic) can be straightforwardly expressed in the framework presented here. Moreover, a Curry–Howard correspondence between proofs in this logic and λ-terms provides a semantic interpretation as a by-product of the process of showing syntactic well-formedness.

Lexical Functional Grammar feature-structures “unification” grammar 

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References

  1. Andrews, A.D., 1982, “The representation of Case in modern Icelandic,” pp. 427–502 in The Mental Representation of Grammatical Relations, J. Bresnan, ed., Cambridge, MA: TheMIT Press.Google Scholar
  2. Bayer, S. and Johnson, M., 1995, “Features and agreement,” pp. 70–76 in The Proceedings of the 33rd Annual Meeting of the Association for Computational Linguistics, San Francisco, CA: Morgan Kaufmann.Google Scholar
  3. Bresnan, J., 1982, “Control and complementation,” pp. 282–390 in The Mental Representation of Grammatical Relations, J. Bresnan, ed., Cambridge, MA: TheMIT Press.Google Scholar
  4. Bresnan, J., Kaplan, R.M., Peters, S., and Zaenen, A., 1982, “Cross-serial dependencies in Dutch,” Linguistic Inquiry 13, 613–635.Google Scholar
  5. Butt, M., Fortmann, C., and Rohrer, C., 1996, “Syntactic analyses for parallel grammars: Auxiliaries and genitive NPs,” in Proceedings of COLING 1996.Google Scholar
  6. Carpenter, B., 1996, Lectures on Type-Logical Semantics, Cambridge, MA: The MIT Press.Google Scholar
  7. Chierchia, G., 1984, “Topics in the syntax and semantics of infinitives and gerunds,” Ph.D. Thesis, University of Massachusetts, Amherst.Google Scholar
  8. Dalrymple, M., 1993, The Syntax of Anaphoric Binding, CSLI Lecture Notes, Vol. 36, Stanford, CA: CSLI Publications.Google Scholar
  9. Dalrymple, M., Lamping, J., Pereira, F., and Saraswat, V., 1995a, “Linear logic for meaning assembly,” pp. 75–93 in Formal Grammar: Proceedings of the Conference of the European Summer School in Logic, Language and Information, Barcelona, Spain, G.V. Morrill and R.T. Oehrle, eds.Google Scholar
  10. Dalrymple, M., Lamping, J., Pereira, F.N.C., and Saraswat, V., 1995b, “Linear logic for meaning assembly,” in Proceedings of CLNLP, Edinburgh.Google Scholar
  11. Dalrymple, M., Lamping, J., Pereira, F.C.N., and Saraswat, V., 1996a, “A deductive account of quantification in LFG,” in Quantifiers, Deduction, and Context, M. Kanazawa, C.J. Piñón, and H. de Swart, eds., Stanford, CA: CSLI Publications.Google Scholar
  12. Dalrymple, M., Lamping, J., Pereira, F.C.N., and Saraswat, V., 1996b, “Intensional verbs without type-raising or lexical ambiguity,” pp. 167–182 in Logic, Language and Computation, J. Seligman and D. Westerståhl, eds., Stanford, CA: CSLI Publications. Also in Proceedings of the Conference on Information-Oriented Approaches to Logic, Language and Computation/Fourth Conference on Situation Theory and Its Applications, Saint Mary' College of California, Moraga, CA, June 1994.Google Scholar
  13. Dalrymple, M., Lamping, J., Pereira, F.C.N., and Saraswat, V., 1997, “Quantifiers, anaphora, and intensionality,” Journal of Logic, Language, and Information 6, 219–273.Google Scholar
  14. Dörre, J., König, E., and Gabbay, D., 1996, “Fibred semantics for feature-based grammar logic,” Journal of Logic, Language and Information 5, 3–4.Google Scholar
  15. Dowty, D.R., 1985, “On recent analyses of the semantics of control,” Linguistics and Philosophy 8(3), 291–332.Google Scholar
  16. Gabbay, D.M., 1994, “Classical vs non-classical logics (the universality of classical logic),” pp. 359–500 in Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 2: Deduction Methodologies, D.M. Gabbay, C.J. Hogger, and J.A. Robinson, eds., Oxford: Oxford University Press.Google Scholar
  17. Girard, J.-Y., 1995, “Linear Logic: Its syntax and semantics,” pp. 1–42 in Advances in Linear Logic, J.-Y. Girard, Y. Lafont, and L. Regnier, eds., Cambridge, England: Cambridge University Press.Google Scholar
  18. Girard, J.-Y., Lafont, Y., and Taylor, P., 1989, Proofs and Types, Cambridge Tracts in Theoretical Computer Science, Vol. 7, Cambridge, England: Cambridge University Press.Google Scholar
  19. Jacobson, P., 1990, “Raising as function composition,” Linguistics and Philosophy 13(4), 423–457.Google Scholar
  20. Johnson, M., 1988, Attribute Value Logic and The Theory of Grammar, CSLI Lecture Notes Series, Vol. 16, Chicago, IL: Chicago University Press.Google Scholar
  21. Johnson, M., 1991, “Features and formulae,” Computational Linguistics 17(2), 131–152.Google Scholar
  22. Johnson, M., 1995, “Logic and feature structures,” pp. 369–380 in Formal Properties of Lexical-Functional Grammar, M. Dalrymple and R.M. Kaplan, eds., CSLI Lecture Notes Series, Stanford, CA: CSLI.Google Scholar
  23. Johnson, M., 1997, “Features as Resources in R-LFG,” in Proceedings of the 1997 LFG Conference, Stanford, CA: CSLI Publications.Google Scholar
  24. Johnson, M., 1998, “Type-driven semantic interpretation and feature dependencies in R-LFG,” in Working with Glue: Resource Accounting and Semantic Interpretation in Lexical Functional Grammar, M. Dalrymple, ed., Cambridge, MA: The MIT Press, to appear.Google Scholar
  25. Johnson, M. and Bayer, S., 1995, “Features and agreement in lambek categorial grammar,” pp. 123–137 in Formal Grammar: Proceedings of the Conference of the European Summer School in Logic, Language and Information, BarcelonaSpain, G.V. Morrill and R.T. Oehrle, eds., Universitat Politècnica de Catalunya.Google Scholar
  26. Kaplan, R. and Maxwell III, J.T., 1988, “Constituent coordination in Lexical-Functional Grammar,” pp. 297–302 in The Proceedings of the 12th International Conference on Computational Linguistics.Google Scholar
  27. Kaplan, R.M. and Bresnan, J., 1982, “Lexical-Functional grammar: A formal system for grammatical representation,” pp. 173–281 in The Mental Representation of Grammatical Relations, J. Bresnan, ed., Cambridge, MA: The MIT Press.Google Scholar
  28. Kaplan, R.M. and Zaenen, A., 1995, “Long-distance dependencies, constituent structure and functional uncertainty,” pp. 137–165 in Formal Issues in Lexical-Functional Grammar, M. Dalrymple, R.M. Kaplan, J.T. Maxwell III, and A. Zaenen, eds., CSLI Lecture Notes Series, Vol. 47, Stanford, CA: CSLI Publications.Google Scholar
  29. Kasper, R.T. and Rounds, W.C., 1990, “The logic of unification in grammar,” Linguistics and Philosophy 13(1), 35–58.Google Scholar
  30. Kehler, A., Dalrymple, M., Lamping, J., and Saraswat, V., 1995, “The semantics of resource-sharing in Lexical-Functional Grammar,” in Proceedings of the 7th Meeting of the European Association for Computational Linguistics, University College Dublin.Google Scholar
  31. König, E., 1995, “Lexical functional grammars and lexical grammars,” Technical report, Institute for Computational Linguistics, Universität Stuttgart.Google Scholar
  32. Maxwell III, J.T. and Kaplan, R.M., 1995, “The interface between phrasal and functional constraints,” pp. 403–430 in Formal Issues in Lexical-Functional Grammar, M. Dalrymple, R.M. Kaplan, J.T. Maxwell III, and A. Zaenen, eds., CSLI Lecture Notes Series, Vol. 47, Stanford, CA: CSLI Publications.Google Scholar
  33. Moortgat, M., 1997, “Categorial type logics,” pp. 93–178 in Handbook of Logic and Language, J. van Benthem and A. ter Meulen, eds., Cambridge, MA: The MIT Press.Google Scholar
  34. Morrill, G.V., 1994, Type-Logical Grammar: Categorial Logic of Signs, Dordrecht: Kluwer Academic Publishers.Google Scholar
  35. Rounds, W.C., 1997, “Feature logics,” pp. 475–533 in Handbook of Logic and Language, J. van Benthem and A. ter Meulen, eds., Cambridge, MA: The MIT Press.Google Scholar
  36. Sag, I.A., 1995, “HPSG problem set 4: Icelandic case,” Technical report, The Center for the Study of Language and Information. Available as http://hpsg.stanford.edu/hpsg/lecturematerials/pset4-icelandic.psGoogle Scholar
  37. Shieber, S.M., 1986, An Introduction to Unification-based Approaches to Grammar, CSLI Lecture Notes Series, Number 4, Chicago, IL: Chicago University Press.Google Scholar
  38. van Benthem, J., 1995, Language in Action: Categories, Lambdas and Dynamic Logic, Cambridge, MA: The MIT Press.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  1. 1.Department of Cognitive and Linguistic SciencesBrown UniversityProvidenceU.S.A

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