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Interpreting Logics of Knowledge in Propositional Dynamic Logic with Converse

机译：用逆向解释命题动态逻辑中的知识逻辑

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摘要

A natural propositional logic of knowledge, common knowledge, and branching time appropriate for reasoning about distributed systems is presented. This logic may be interpreted in Propositional Dynamic Logic with Converse (PDLC) making the relationship between protocol models and general Kripke models precise and showing that PDLC already suffices for a certain amount of reasoning about knowledge in distributed systems. It follows that satisfiability for propositional logic of branching time remains EMPTIME complete with the addition of any combination of knowledge and common knowledge operators. Finally, the validity or satisfiability of a formula involving two or more participants is not affected by restricting attention to protocol involving just those participants explicitly mentioned in the formula. Keywords: Logic of knowledge; Distributed system; Modal logic; Propositional dynamic logic.

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