Martin Stokhof

With a few notable exceptions formal semantics, as it originated from the seminal work of Richard Montague, Donald Davidson, Max Cresswell, David Lewis and others, in the late sixties and early seventies of the previous century, does not consider Wittgenstein as one of its ancestors. That honour is bestowed on Frege, Tarski, Carnap. And so it has been in later developments. Most introductions to the subject will refer to Frege and Tarski (Carnap less frequently) —in addition to the pioneers just mentioned, of course— , and discuss the main elements of their work that helped shape formal semantics in some detail. But Wittgenstein is conspicuously absent whenever the history of the subject is mentioned (usually briefly, if at all).

In Groenendijk & Stokhof [1989] a system of dynamic predicate logic (DPL) was developed, as a compositional alternative for classical discourse representation theory (DRT ). DPL shares with DRT the restriction of being a first-order system. In the present paper, we are mainly concerned with overcoming this limitation. We shall define a dynamic semantics for a typed language with λ-abstraction which is compatible with the semantics DPL specifies for the language of first-order predicate logic. We shall propose to use this new logical system as the semantic component of a Montague-style grammar (referred to as dynamic Montague grammar, DMG), which will enable us to extend the compositionality of DPL to the subsentential level. Furthermore, we shall extend this analysis also in this sense that we shall add new, dynamic interpretations for logical constants which in DPL were treated in a static fashion. This will substantially increase the descriptive coverage of DMG.