Telling Lies in Process Algebra

Epistemic logic is a powerful formalism for reasoning about communication protocols, particularly in the setting with dishonest agents and lies. Operational frameworks such as algebraic process calculi, on the other hand, are powerful formalisms for specifying the narrations of communication protocols. We bridge these two powerful formalisms by presenting a process calculus in which lies can be told. A lie in our framework is a communicated message that is pretended to be a different message (or nothing at all). In our formalism, we focus on what credulous rational agents can infer about a particular run if they know the protocol beforehand. We express the epistemic properties of such specifications in a rich extension of modal µ-calculus with the belief modality and define the semantics of our operational models in the semantic domain of our logic. We formulate and prove criteria that guarantee belief consistency for credulous agents.

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