Graded Monad Coalgebras for Continuous-Time Transition Systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911657538617344 |
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| author | Di Lavore, Elena Forster, Jonas Román, Mario |
| author_facet | Di Lavore, Elena Forster, Jonas Román, Mario |
| contents | Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of graded coalgebras-including graded distributive laws between graded monads-and we give conditions for the existence of terminal coalgebras. We define both branching-time and trace semantics, linking them to recent work on Feller-Dynkin processes. Finally, we develop coalgebraic modal logics for both process semantics and state criteria for invariance and expressivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06268 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graded Monad Coalgebras for Continuous-Time Transition Systems Di Lavore, Elena Forster, Jonas Román, Mario Logic in Computer Science 68Q87 F.4.1 Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of graded coalgebras-including graded distributive laws between graded monads-and we give conditions for the existence of terminal coalgebras. We define both branching-time and trace semantics, linking them to recent work on Feller-Dynkin processes. Finally, we develop coalgebraic modal logics for both process semantics and state criteria for invariance and expressivity. |
| title | Graded Monad Coalgebras for Continuous-Time Transition Systems |
| topic | Logic in Computer Science 68Q87 F.4.1 |
| url | https://arxiv.org/abs/2605.06268 |