Reasoning about knowledge
Logic in computer science: modelling and reasoning about systems
Logic in computer science: modelling and reasoning about systems
Actions and resources in epistemic logic
Actions and resources in epistemic logic
Dynamic Epistemic Logic
Tableaux for Public Announcement Logic
Journal of Logic and Computation
Coalgebraic epistemic update without change of model
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Electronic Notes in Theoretical Computer Science (ENTCS)
Cut elimination in nested sequents for intuitionistic modal logics
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
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We develop a cut-free nested sequent calculus as basis for a proof search procedure for an intuitionistic modal logic of actions and propositions. The actions act on propositions via a dynamic modality (the weakest precondition of program logics), whose left adjoint we refer to as “update” (the strongest postcondition). The logic has agent-indexed adjoint pairs of epistemic modalities: the left adjoints encode agents' uncertainties and the right adjoints encode their beliefs. The rules for the “update” modality encode learning as a result of discarding uncertainty. We prove admissibility of Cut, and hence the soundness and completeness of the logic with respect to an algebraic semantics. We interpret the logic on epistemic scenarios that consist of honest and dishonest communication actions, add assumption rules to encode them, and prove that the calculus with the assumption rules still has the admissibility results. We apply the calculus to encode (and allow reasoning about) the classic epistemic puzzles of dirty children (a.k.a. “muddy children”) and drinking logicians and some versions with dishonesty or noise; we also give an application where the actions are movements of a robot rather than announcements.