Explicit Evidence Systems with Common Knowledge

TitleExplicit Evidence Systems with Common Knowledge
Publication TypeTechnical Reports
Year of Publication2010
AuthorsBucheli, S, Kuznets, R, Studer, T
AbstractJustification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs $\mathsf{LP}$. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of $\mathsf{LP}$. We discuss the relationship of our logic to the multi-agent modal logic $\mathsf{S4}$ with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic.