Abstract
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.
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References
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.
BarwiseJ., 1987, “Noun phrases, generalized quantifiers and anaphora,” in Generalized Quantifiers / Linguistic and Logical Approaches, P.Gärdenfors, ed., Dordrecht: Reidel, pp. 1–29.
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.
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).
EvansG., 1980, “Pronouns,” Linguistic Inquiry 11, 337–362.
GeachP.T., 1962, Reference and Generality / An Examination of Some Medieval and Modern Theories, Ithaca and London: Cornell University Press, (Third revised edition: 1980).
GroenendijkJ. and StokhofM., 1991, “Dynamic predicate logic,” Linguistics and Philosophy 14, 39–100.
HarelD., 1984, “Dynamic logic,” in Handbook of Philosophical Logic, Vol. II, D.Gabbay and F.Guenthner, eds., Dordrecht: Reidel, pp. 497–604.
HeimI., 1990, “E-type pronouns and donkey anaphora,” Linguistics and Philosophy 13, 137–177.
HoareC.A.R., 1969, “An axiomatic basis for computer programming,” Communications of the ACM 12, No. 10, 567–580, 583.
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.
Kamp, H. and Reyle, U., 1990, From Discourse to Logic, Manuscript, Institute for Computational Linguistics, University of Stuttgart.
RobertsC., 1989, “Modal subordination and pronominal anaphora in discourse,” Linguistics and Philosophy 12, 683–721.
RussellB., 1905, “On denoting,” Mind 14, 479–493.
van Benthem, J., 1990, “General dynamics,” ITLI report, Amsterdam, (to appear in Theoretical Linguistics).
WesterståhlD., 1989, “Quantifiers in formal and natural languages,” in Handbook of Philosophical Logic, Vol. IV, Gabbay and Guenthner, eds., Dordrecht: Reidel, pp. 1–131.
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Van Eijck, J., De Vries, FJ. Dynamic interpretation and hoare deduction. J Logic Lang Inf 1, 1–44 (1992). https://doi.org/10.1007/BF00203385
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DOI: https://doi.org/10.1007/BF00203385