Expressive Logics for Coinductive Predicates
Logic in Computer Science
2023-06-22 v4
Abstract
The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. We formulate when a logic fully characterises a coinductive predicate on coalgebras, by providing suitable notions of adequacy and expressivity, and give sufficient conditions on the semantics. The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata.
Keywords
Cite
@article{arxiv.2006.12465,
title = {Expressive Logics for Coinductive Predicates},
author = {Clemens Kupke and Jurriaan Rot},
journal= {arXiv preprint arXiv:2006.12465},
year = {2023}
}