Graded Monad Coalgebras for Continuous-Time Transition Systems
Logic in Computer Science
2026-05-08 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2605.06268,
title = {Graded Monad Coalgebras for Continuous-Time Transition Systems},
author = {Elena Di Lavore and Jonas Forster and Mario Román},
journal= {arXiv preprint arXiv:2605.06268},
year = {2026}
}