Explicit Evidence Systems with Common Knowledge

Justification logics are epistemic logics that explicitly include justifications for agents’ knowledge. We present a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. A Kripke-style semantics similar to Fitting’s semantics for the Logic of Proofs LP is defined and soundness and completeness with respect to it are shown along with the finite model property. Furthermore, we demonstrate that our logic is a conservative extension of Yavorskaya’s minimal bimodal explicit evidence logic, a two-agent version of LP. We discuss the relationship to multi-agent modal logic S4 with common knowledge. Finally, as an illustration we give a brief analysis of the problem of coordinated attack in the new language.