Reasoning about knowledge
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
The temporal logic of coalgebras via Galois algebras
Mathematical Structures in Computer Science
A compositional approach to defining logics for coalgebras
Theoretical Computer Science - Selected papers of CMCS'03
Actions and resources in epistemic logic
Actions and resources in epistemic logic
Modular Games for Coalgebraic Fixed Point Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
Aximo: Automated Axiomatic Reasoning for Information Update
Electronic Notes in Theoretical Computer Science (ENTCS)
Coalgebraic announcement logics
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
ACM Transactions on Computational Logic (TOCL)
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We present a coalgebraic semantics for reasoning about information update in multi-agent systems. The novelty is that we have one structure for both states and actions and thus our models do not involve the "change-of-model" phenomena that arise when using Kripke models. However, we prove that the usual models can be constructed from ours by categorical adjunction. The generality and abstraction of our coalgebraic model turns out to be extremely useful in proving preservation properties of update. In particular, we prove that positive knowledge is preserved and acquired as a result of epistemic update. We also prove common and nested knowledge properties of epistemic updates induced by specific epistemic actions such as public and private announcements, lying, and in particular unsafe actions of security protocols. Our model directly gives rise to a coalgebraic logic with both dynamic and epistemic modalities. We prove a soundness and completeness result for this logic, and illustrate the applicability of the logic by deriving knowledge properties of a simple security protocol.