2017/07/25 by Kohei Kishida
Computer Science · Mathematics · #Advanced Algebra and Logic #Categorical variable #Duality (order theory) #Epistemic modal logic #Kripke semantics #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Modal logic #Multimodal logic #Object (grammar) #Perspective (graphical) #Semantics (computer science) #cs.LO #math.LO
paper · pdf · doi:10.4204/eptcs.251.26
published as EPTCS 251, 2017, pp. 353-372 · In Proceedings TARK 2017, arXiv:1707.08250
openalex publication_date 2017/07/25 · arxiv created 2017/07/27 · arxiv updated 2017/07/28 · openalex created_date 2017/07/31 · openalex updated_date 2026/08/05
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.