Categories for dynamic epistemic logic
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 categori...
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| Format: | Conference item |
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Electronic Proceedings in Theoretical Computer Science
2017
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| _version_ | 1826269671819575296 |
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| author | Kishida, K |
| author_facet | Kishida, K |
| author_sort | Kishida, K |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T21:28:45Z |
| format | Conference item |
| id | oxford-uuid:43f5c1d2-75ac-4fb0-b3b9-b32e2d1a9c1a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:28:45Z |
| publishDate | 2017 |
| publisher | Electronic Proceedings in Theoretical Computer Science |
| record_format | dspace |
| spelling | oxford-uuid:43f5c1d2-75ac-4fb0-b3b9-b32e2d1a9c1a2022-03-26T14:58:42ZCategories for dynamic epistemic logicConference itemhttp://purl.org/coar/resource_type/c_5794uuid:43f5c1d2-75ac-4fb0-b3b9-b32e2d1a9c1aSymplectic Elements at OxfordElectronic Proceedings in Theoretical Computer Science2017Kishida, KThe 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. |
| spellingShingle | Kishida, K Categories for dynamic epistemic logic |
| title | Categories for dynamic epistemic logic |
| title_full | Categories for dynamic epistemic logic |
| title_fullStr | Categories for dynamic epistemic logic |
| title_full_unstemmed | Categories for dynamic epistemic logic |
| title_short | Categories for dynamic epistemic logic |
| title_sort | categories for dynamic epistemic logic |
| work_keys_str_mv | AT kishidak categoriesfordynamicepistemiclogic |