Bilattice Public Announcement Logic

Building on recent work on bilattice modal logic and extensions of public announcement logic to a non-classical setting, we introduce a dynamic epistemic logic having the logic of modal bilattices as propositional support. Bilattice logic is both inconsistency-tolerant and paracomplete, thus suited for applications in contexts with multiple sources of information, where one may have to deal with lacking as well as potentially contradictory evidence. We introduce an algebra-based semantics for bilattice public announcement logic as well as a relational semantics based on manyvalued Kripke models. We show via duality that the two semantics are equivalent and axiomatize the resulting logic by means of a Hilbert-style calculus. Our results and methodology extend recent work on non-classical dynamic epistemic logics such as intuitionistic public announcement logic.

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