X-2016-02: Bisimulation for conditional modalities

X-2016-02: Baltag, Alexandru and Ciná, Giovanni (2016) Bisimulation for conditional modalities. [Report]

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Abstract

We give a general definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence. We describe how this framework specializes to unary modalities and further investigate the operators and semantics to which these results apply. First, we show that our models encompass both Grove’s sphere models and Gabbay’s models for non- monotonic reasoning. Second, 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. Third, we treat relativized common knowledge, underlining how the same observations still hold for a different modality in a different semantics. Finally, we show the flexibility of the approach by generalizing it to multi-agent systems, encompassing the case of multi-agent plausibility models and suggesting how to cover group conditional belief.

Item Type:	Report
Report Nr:	X-2016-02
Series Name:	Technical Notes (X) Series
Year:	2016
Uncontrolled Keywords:	Bisimulation, Modal logic, Conditional logic
Subjects:	Logic
Depositing User:	Giovanni Cina
Date Deposited:	12 Oct 2016 14:38
Last Modified:	12 Oct 2016 14:38
URI:	https://eprints.illc.uva.nl/id/eprint/694

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