Building epistemic logic from observations and public announcements
Résumé
We study an epistemic logic where knowledge is built from what the agents observe (including higher-order visibility) and what the agents learn from public announcements. This fixes two main drawbacks of previous observability-based approaches where who sees what is common knowledge and where the epistemic operators distribute over disjunction. The latter forbids the modeling of most of the classical epistemic problems, starting with the muddy children puzzle. We integrate a dynamic dimension where both facts of the world and the agents' observability can be modified by assignment programs. We provide a sound and complete axiomatization of the logic and establish that the model checking problem is PSPACE-complete.
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