Dynamic interpretation and hoare deduction

  • Jan Van Eijck
  • Fer-Jan De Vries


In this paper we present a dynamic assignment language which extends the dynamic predicate logic of Groenendijk and Stokhof [1991: 39–100] with ι assignment and with generalized quantifiers. The use of this dynamic assignment language for natural language analysis, along the lines of o.c. and [Barwise, 1987: 1–29], is demonstrated by examples. We show that our representation language permits us to treat a wide variety of ‘donkey sentences’: conditionals with a donkey pronoun in their consequent and quantified sentences with donkey pronouns anywhere in the scope of the quantifier. It is also demonstrated that our account does not suffer from the so-called proportion problem.

Discussions about the correctness or incorrectness of proposals for dynamic interpretation of language have been hampered in the past by the difficulty of seeing through the ramifications of the dynamic semantic clauses (phrased in terms of input-output behaviour) in non-trivial cases. To remedy this, we supplement the dynamic semantics of our representation language with an axiom system in the style of Hoare. While the representation languages of barwise and Groenendijk and Stokhof were not axiomatized, the rules we propose form a deduction system for the dynamic assignment language which is proved correct and complete with respect to the semantics.

Finally, we define the static meaning of a program π of the dynamic assignment language as the weakest condition ϕ such that π terminates successfully on all states satisfying ϕ, and we show that our calculus gives a straightforward method for finding static meanings of the programs of the representation language.

Key words

semantics of natural language dynamic interpretation Hoare logic knowledge representation languages 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. AptK.R., 1981, “Ten years of Hoare's logic: A survey — Part I,” ACM Transactions on Programming Languages and Systems 3, No. 4, 431–483.Google Scholar
  2. BarwiseJ., 1987, “Noun phrases, generalized quantifiers and anaphora,” in Generalized Quantifiers / Linguistic and Logical Approaches, P.Gärdenfors, ed., Dordrecht: Reidel, pp. 1–29.Google Scholar
  3. Chierchia, G., 1991, “Anaphora and dynamic logic,” in Quantification and Anaphora I, M. Stokhof, J. Groenendijk, and D. Beaver, eds., Edinburgh: (DYANA deliverable R2.2.A), pp. 37–78.Google Scholar
  4. van Eijck, J., 1991, “The dynamics of description,” Amsterdam: CWI Technical Report CS-R9143, (also in: Computational Linguistics in the Netherlands; Papers from the First CLIN Meeting, T. van der Wouden and W. Sijtsma, eds., Utrecht: OTS Working Papers OTS-WP-CL-91-001, pp. 33–58).Google Scholar
  5. EvansG., 1980, “Pronouns,” Linguistic Inquiry 11, 337–362.Google Scholar
  6. GeachP.T., 1962, Reference and Generality / An Examination of Some Medieval and Modern Theories, Ithaca and London: Cornell University Press, (Third revised edition: 1980).Google Scholar
  7. GroenendijkJ. and StokhofM., 1991, “Dynamic predicate logic,” Linguistics and Philosophy 14, 39–100.Google Scholar
  8. HarelD., 1984, “Dynamic logic,” in Handbook of Philosophical Logic, Vol. II, D.Gabbay and F.Guenthner, eds., Dordrecht: Reidel, pp. 497–604.Google Scholar
  9. HeimI., 1990, “E-type pronouns and donkey anaphora,” Linguistics and Philosophy 13, 137–177.Google Scholar
  10. HoareC.A.R., 1969, “An axiomatic basis for computer programming,” Communications of the ACM 12, No. 10, 567–580, 583.Google Scholar
  11. KampH., 1981, “A theory of truth and semantic representation,” in Formal Methods in the Study of Language, Groenendijk et al., eds., Amsterdam: Mathematisch Centrum, pp. 277–322.Google Scholar
  12. Kamp, H. and Reyle, U., 1990, From Discourse to Logic, Manuscript, Institute for Computational Linguistics, University of Stuttgart.Google Scholar
  13. RobertsC., 1989, “Modal subordination and pronominal anaphora in discourse,” Linguistics and Philosophy 12, 683–721.Google Scholar
  14. RussellB., 1905, “On denoting,” Mind 14, 479–493.Google Scholar
  15. van Benthem, J., 1990, “General dynamics,” ITLI report, Amsterdam, (to appear in Theoretical Linguistics).Google Scholar
  16. WesterståhlD., 1989, “Quantifiers in formal and natural languages,” in Handbook of Philosophical Logic, Vol. IV, Gabbay and Guenthner, eds., Dordrecht: Reidel, pp. 1–131.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Jan Van Eijck
    • 1
    • 2
  • Fer-Jan De Vries
    • 3
  1. 1.CWIAmsterdamThe Netherlands
  2. 2.OTSUtrechtThe Netherlands
  3. 3.CWIAmsterdamThe Netherlands

Personalised recommendations