Dynamic Interpretation and Hoare Deduction

In this paper we present a dynamic assignment language which extends the dynamic predicate logic of Groenendijk & Stokhof [1991: 39{100] with assignment and with generalized quanti ers. 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 quanti ed sentences with donkey pronouns anywhere in the scope of the quanti er. It is also demonstrated that our account does not su er 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 di culty of seeing through the rami cations 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 & 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 de ne the static meaning of a program of the dynamic assignment language as the weakest condition ' such that terminates successfully on all states satisfying ', and we show that our calculus gives a straightforward method for nding static meanings of the programs of the representation language.