| Summary: | 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.
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