A Categorical Approach to Coalgebraic Fixpoint Logic
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917655055695872 |
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| author | Schoen, Ezra Kupke, Clemens Rot, Jurriaan Turkenburg, Ruben |
| author_facet | Schoen, Ezra Kupke, Clemens Rot, Jurriaan Turkenburg, Ruben |
| contents | We define a framework for incorporating alternation-free fixpoint logics into the dual-adjunction setup for coalgebraic modal logics. We achieve this by using order-enriched categories. We give a least-solution semantics as well as an initial algebra semantics, and prove they are equivalent. We also show how to place the alternation-free coalgebraic $μ$-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Categorical Approach to Coalgebraic Fixpoint Logic Schoen, Ezra Kupke, Clemens Rot, Jurriaan Turkenburg, Ruben Logic in Computer Science We define a framework for incorporating alternation-free fixpoint logics into the dual-adjunction setup for coalgebraic modal logics. We achieve this by using order-enriched categories. We give a least-solution semantics as well as an initial algebra semantics, and prove they are equivalent. We also show how to place the alternation-free coalgebraic $μ$-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality. |
| title | A Categorical Approach to Coalgebraic Fixpoint Logic |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2405.00237 |