The Donkey and the Monoid. Dynamic Semantics with Control Elements

Abstract

Dynamic Predicate Logic (DPL) is a variant of Predicate Logic introduced by Groenendijk and Stokhof. One rationale behind the introduction of DPL is that it is closer to Natural Language than ordinary Predicate Logic in the way it treats scope.

In this paper I develop some variants of DPL that can more easily approximate Natural Language in some further aspects. Specifically I add flexibility in the treatment of polarity and and some further flexibility in the treatment of scope.

I develop a framework that is intended to encourage further experimentation with alternative variants of DPL. In this framework the new meanings are, roughly,indexed sets of old meanings. The indices can be viewed as "files'' or "storage devices.''Each such file supports a separate "information stream.''The interaction of the new meanings is "programmed'' with the help of certain monoids acting on the indices. The construction of the new meanings can be viewed as an application of the Grothendieck Construction to monoids.