Logic of (Common or Distributed) Knowledge

TL;DR

This paper extends epistemic logic to include complex combinations of common and distributed knowledge, and explores their dynamic updates through arbitrary reading events, providing axiomatizations with proofs of soundness and completeness.

Contribution

It introduces a generalized epistemic logic for combined knowledge modalities and develops axiomatic systems for their dynamic updates, filling a gap in formal reasoning about complex knowledge states.

Findings

Axiomatization of combined knowledge logics

Soundness and completeness proofs for the proposed systems

Framework for dynamic updates via reading events

Abstract

In this paper, we generalize epistemic logic so that it can help reason about ways of combining common knowledge and distributed knowledge such as "common distributed knowledge", "distributed common knowledge", "distributed common distributed knowledge" and so on. Moreover, we study the logic of its dynamic update by arbitrary reading events. We axiomatize these logics and prove their soundness and completeness.