Categories for dynamic epistemic logic - Kishida, K (Electronic Proceedings in Theoretical Computer Science, 2017)
The primary goal of this paper is to recast the conventional semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and a category of Kripke frames, with some reference to duality results. Using these categories, we then reformulate the semantics of DEL in a more categorical and algebraic form. Several virtues of the new formulation will be demonstrated: The DEL idea of updating a model into another is captured naturally by the categorical perspective—which emphasizes a family of objects and structural relationships among them, as opposed to a single object and structure on it. Also, the categorical semantics of DEL can be merged straightforwardly with a standard categorical semantics for first-order logic, providing a new semantics for first-order DEL.