Dynamic Squares

Abstract

This paper examines various propositional logics in which the dynamic implication connective (discussed in Groenendijk and Stokhof's (1992) Dynamic Predicate Logic and Kamp's (1981) Discourse Representation Theory) plays the central role. Our approach is modal: the basic idea is to view as a binary modal operator in a two dimensional modal logic. Two dimensional modal logics are systems in which formulas are evaluated at pairs of points. Such logics provide natural setting for studying, for we can think of the first point in the pair as an input state, and the second point in the pair as an output state.