Bisimulation for Conditional Modalities

Studia Logica 106 (1):1-33 (2018)
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Abstract

We give a definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence, generalizing the Hennessy–Milner Theorem to a wide class of conditional operators. We further investigate the operators and semantics to which these results apply. First, we show how to derive a solid notion of bisimulation for conditional belief, behaving as desired both on plausibility models and on evidence models. These novel definitions of bisimulations are exploited in a series of undefinability results. Second, we treat relativized common knowledge, underlining how the same results still hold for a different modality in a different semantics. Third, we show the flexibility of the approach by generalizing it to multi-agent systems, encompassing the case of multi-agent plausibility models.

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Author Profiles

Alexandru Baltag
University of Amsterdam
Giulia Cina
Università degli Studi di Firenze

References found in this work

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Two modellings for theory change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.
Dynamic logic for belief revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.

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