Journal of Logic, Language and Information

, Volume 7, Issue 1, pp 21–52 | Cite as

Contexts in Dynamic Predicate Logic

  • Albert Visser
Article

Abstract

In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give a characterization of the relations on assignments that can be generated by composition from tests and random resettings in the case that we are working over an infinite domain. These relations are precisely the ones expressible in DPL if we allow ourselves arbitrary tests as a starting point. We discuss some possible extensions of DPL and the way these extensions interact with our notion of context.

Context dynamics Predicate Logic relation resetting register variable expressability definability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barendregt, H.P., 1984, The Lambda Calculus, Amsterdam: North-Holland.Google Scholar
  2. Barendregt, H.P., 1991, “Functional programming and lambda calculus,” pp. 321–363 in Formal Models and Semantics, Handbook of Theoretical Computer Science, Vol. B, J. van Leeuwen, ed., Amsterdam: Elsevier.Google Scholar
  3. Barendregt, H.P., 1992, “Lambda calculi with types,” pp. 117–309 in Handbook of Logic in Computer Science, Vol. 2, S. Ambramsky, D.M. Gabbay, and T.S.E. Maibaum, eds., Oxford: Clarendon.Google Scholar
  4. Groenendijk, J. and Stokhof, J., 1991, “Dynamic predicate logic,” Linguistics and Philosophy 14, 39–100.Google Scholar
  5. Groenendijk, J., Stokhof, M., and Veltman, F., 1996, “Coreference and modality,” pp. 179–213 in Handbook of Contemporary Semantic Theory, S. Lappin, ed., Oxford: Blackwell.Google Scholar
  6. Heim, I., 1983, “File change semantics and the familiarity theory of definiteness,” pp. 164–189 in Meaning, Use and Interpretation of Language, R. Bäuerle, C. Schwarze, and A. von Stechow, eds., Berlin: De Gruyter.Google Scholar
  7. Hollenberg, M. and Vermeulen, C.F.M., 1994, “Counting variables in a dynamic setting,” Logic Group Preprint Series LGPS-125, Department of Philosophy, Utrecht University. Also in: Journal of Logic and Computation 6, 1996, 725–744.Google Scholar
  8. Jacobs, B., 1991, “Categorical type theory,” Ph.D. Thesis, Nijmegen University.Google Scholar
  9. Kamp, H., 1981, “A theory of truth and semantic representation,” pp. 1–41 in Truth, Interpretation and Information, J. Groenendijk, T. Jansen, and M. Stokhof, eds., Dordrecht: Foris.Google Scholar
  10. Klop, J.W., 1992, “Term rewriting systems,” pp. 1–116 in Handbook of Logic in Computer Science, Vol. 2, S. Ambramsky, D.M. Gabbay, and T.S.E. Maibaum, eds., Oxford: Clarendon.Google Scholar
  11. Mitchell, J., 1991, “Type systems for programming languages,” pp. 365–458 in Formal Models and Semantics, Handbook of Theoretical Computer Science, Vol. B, J. van Leeuwen, ed., Amsterdam: Elsevier.Google Scholar
  12. Muskens, R., 1991, “Anaphora and the logic of change,” pp. 414–430 in '90, European Workshop on Logics in AI, J. van Eijck, ed., Springer Lecture Notes, Vol. 478, Berlin: SpringerVerlag.Google Scholar
  13. Nederpelt, R., Geuvers, J.H., and de Vrijer, R.C., eds., 1994, Selected Papers on Automath, Amsterdam: North Holland.Google Scholar
  14. Troelstra, A.S. and van Dalen, D., 1988a, Constructivism in Mathematics, Vol. 1, Studies in Logic and the Foundations of Mathematics, Vol. 121, Amsterdam: North Holland.Google Scholar
  15. Troelstra, A.S. and van Dalen, D., 1988b, Constructivism in Mathematics, Vol. 2, Studies in Logic and the Foundations of Mathematics, Vol. 123, Amsterdam: North Holland.Google Scholar
  16. Veltman, F., 1996, “Defaults in update semantics,” Journal of Philosophical Logic 25, 221–261.Google Scholar
  17. Vermeulen, C.F.M., 1993, “Sequence semantics for dynamic predicate logic,” Journal of Logic, Language and Information 2, 217–254.Google Scholar
  18. Vermeulen, C.F.M., 1995, “Merging without mystery, variables in dynamic semantics,” Journal of Philosophical Logic 24, 405–450.Google Scholar
  19. Visser, A., 1994, “Actions under presuppositions,” pp. 196–233, in Logic and Information Flow, J. van Eijck and A. Visser, eds., Cambridge, MA: MIT Press.Google Scholar
  20. Visser, A., 1995, “Dynamic discourse denotations,” Lecture Notes for the Department of Philosophy, University of Utrecht, and the Department of Mathematics and Computer Science, University of Amsterdam.Google Scholar
  21. Visser, A. and Vermeulen, C., 1996, “Dynamic bracketing and discourse representation,” Notre Dame Journal of Formal Logic 37, 321–365.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Albert Visser
    • 1
  1. 1.Department of PhilosophyUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations