Abstract
Logics of knowledge have important applications for reasoning about security protocols and multi-agent systems. We extend the semantics for the logic of necessity with local propositional quantification \({\mathcal L}\)([],∃,∃1,...,∃ k ) introduced in [4] to allow reasoning about knowledge in more general (non-hierarchical) systems. We show that these new semantics preserve the properties of knowledge in a multi-agent system, give a significant and useful increase in expressivity and most importantly, have a decidable satisfiability problem. The new semantics interpret propositional (local and non-local) quantification with respect to bisimulations, and the satisfiability problem is shown to be solvable via an embedding into the temporal logic, QCTL.
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French, T. (2003). Decidability of Propositionally Quantified Logics of Knowledge. In: Gedeon, T.(.D., Fung, L.C.C. (eds) AI 2003: Advances in Artificial Intelligence. AI 2003. Lecture Notes in Computer Science(), vol 2903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24581-0_30
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DOI: https://doi.org/10.1007/978-3-540-24581-0_30
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