Exploring logical dynamics
First-order modal logic
Modal logic
Modal model theory
Dynamic Epistemic Logic
Algebraic semantics and model completeness for intuitionistic public announcement logic
LORI'11 Proceedings of the Third international conference on Logic, rationality, and interaction
Public announcements under sheaves
JSAI-isAI'12 Proceedings of the 2012 international conference on New Frontiers in Artificial Intelligence
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We study some mathematical aspects of public announcement logic (PAL) and its several variants. By a model-theoretic approach, we explore van Benthem's result that uses recursion axioms to characterize the submodel operation, and show some model-theoretic results on the respecting phenomena. The second approach to understand public announcements is algebraic. Based on a joint work with A. Palmigiano and M. Sadrzadeh, we treat public announcements as devices for getting a new quotient algebra updated by an element in the original one. Then we show the algebraic soundness and completeness result for PAL and generalize this approach to PAL extension of epistemic intuitionistic modal logic. Finally, we give some observations on the PAL extensions of first-order logic as well as epistemic predicate modal logic.