Distributed Knowledge Justification Logics

Abstract

Justification logics are a family of modal epistemic logics which enables us to reasoning about justifications and evidences. In this paper, we introduce evidence-based multi-agent distributed knowledge logics, called distributed knowledge justification logics. The language of our justification logics contain evidence-based knowledge operators for individual agents [InlineEquation not available: see fulltext.] and for distributed knowledge [InlineEquation not available: see fulltext.], which are interpreted respectively as "t is a justification that agent i accepts for F", and "t is a justification that all agents accept for F if they combine their knowledge and justifications". We study basic properties of our logics and prove the conservativity of distributed knowledge justification logics over multi-agent justification logics. We present Kripke style models, pseudo-Fitting and Fitting models, as well as Mkrtychev models (single world Fitting models) and prove soundness and completeness theorems. We also find a class of Fitting models which satisfies the principle of full communication. Finally, we establish the realization theorem, which states that distributed knowledge justification logics can be embedded into the modal distributed knowledge logics, and vise versa.