Exemplaric Expressivity of Modal Logics
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Bart Jacobs and Ana Sokolova
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Abstract:
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This paper 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 paper.
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