- Bisimulation for conditional modalities
- Studia Logica
- Volume | Issue number
- 106 | 1
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
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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