9 February 2009, PROSE Colloquium, Ana Sokolova

In this talk I will report on a joint work with Bart Jacobs on examples of expressivity of modal logics. We investigate 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 too. 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 this work. In addition, we observed an interesting comparison of the mentioned types of systems, in particular of Markov chains and Markov processes.

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