Coalgebraic Logic over Measurable Spaces: Behavioral and Logical Equivalence
Electronic Notes in Theoretical Computer Science (ENTCS)
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Electronic Notes in Theoretical Computer Science (ENTCS)
Coalgebraic logic over general measurable spaces ??? a survey
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Electronic Notes in Theoretical Computer Science (ENTCS)
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This article investigates expressivity of modal logics for transition systems, multitransition systems, Markov chains and Markov processes, as coalgebras of the powerset, finitely supported multiset, finitely supported distribution and measure functor, respectively. Expressivity means that logically indistinguishable states, satisfying the same formulas, are behaviourally indistinguishable. The investigation is based on the framework of dual adjunctions between spaces and logics and focuses on a crucial injectivity property. The approach is generic both in the choice of systems and modalities, and in the choice of a ‘base logic’. Most of these expressivity results are already known, but the applicability of the uniform setting of dual adjunctions to these particular examples is what constitutes the contribution of the article.