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Epistemic Updates on Algebras
October 14, 2015 @ 2:00 pm - 4:00 pm
The Logic of Epistemic Actions and Knowledge is an expansion of classical modal logic introduced by A. Baltag, L. S. Moss and S. Solecki as a framework for reasoning about knowledge in a dynamic logic setting. A. Kurz and A. Palmigiano recently showed that duality theory provides a flexible framework for modelling epistemic changes, which allows one to develop dynamic epistemic logics on a propositional basis that is weaker than classical logic (e.g. an intuitionistic basis).
In this talk we explain how the techniques of Kurz and Palmigiano can be further extended to define and axiomatize a bilattice-based Logic of Epistemic Actions and Knowledge. Our propositional basis is a modal expansion of the well-known four-valued logic of Belnap and Dunn, which is a system designed for handling inconsistent as well as potentially conflicting information. These features, we believe, make our framework particularly promising from a computer science perspective.