Dynamic interpretation and hoare deduction
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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 wordssemantics of natural language dynamic interpretation Hoare logic knowledge representation languages
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