Dynamic Epistemic Logic as a Substructural Logic

Abstract

Dynamic Epistemic Logic (DEL) is an influential logical framework for reasoning about the dynamics of beliefs and knowledge. It has been related to older and more established logical frameworks. Despite these connections, DEL remains, arguably, a rather isolated logic in the vast realm of non-classical logics and modal logics. This is problematic if logic is to be viewed ultimately as a unified and unifying field and if we want to avoid that DEL goes on “riding off madly in all directions” (a metaphor used by van Benthem about logic in general). In this article, we show that DEL can be redefined naturally and meaningfully as a two-sorted substructural logic. In fact, it is even one of the most primitive substructural logics since it does not preserve any of the structural rules. Moreover, the ternary semantics of DEL and its dynamic interpretation provides a conceptual foundation for the Routley & Meyer’s semantics of substructural logics.