The primary goal of this paper is to recast the semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and categories of Kripke frames, with particular emphasis on the duality between relations and adjoint homomorphisms. 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 semantics for first-order DEL.
|Original language||English (US)|
|Number of pages||20|
|Journal||Electronic Proceedings in Theoretical Computer Science, EPTCS|
|State||Published - Jul 25 2017|
|Event||16th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2017 - Liverpool, United Kingdom|
Duration: Jul 24 2017 → Jul 26 2017
ASJC Scopus subject areas