TR-2007025: Public Communication in Justification Logic

Justification Logic is the study of a family of logics used to reason about justified true belief. Dynamic Epistemic Logic is the study of a family of logics obtained by adding various kinds of communication to the language of multi-modal logic, yielding languages for reasoning about communication and true belief. This paper is a first-step in merging these two areas, in that it brings the most basic kind of communication studied in Dynamic Epistemic Logic—the public announcement—over to Justification Logic. This gives us a language for reasoning about public announcements and justified true belief. After giving an overview of Justification Logic, the paper introduces a notion of bisimulation for Justification Logic. Bisimulation allows us to study the affect on language expressivity when we add various kinds of communication to the language. Among a number of expressivity results, we show that adding public announcements to the language of Justification Logic strictly increases language expressivity. This stands in contrast to the Plaza-Gerbrandy Theorem, which states that adding public announcements to multi-modal logic does not increase language expressivity. This leads us to extend the language of Justification Logic in order to provide a Plaza-Gerbrandy analog of multi-modal logic that we can use to reason about justified true belief.