Evidence-Based Common Knowledge

In this paper we introduce a new type of knowledge operator, called evidencebased knowledge, intended to capture the constructive core of common knowledge. An evidence-based knowledge system is obtained by augmenting a multi-agent logic of knowledge with a system of evidence assertions t :φ (“t is an evidence for φ”) based on the following plausible assumptions: 1) each axiom has evidence; 3) evidence is checkable; 3) any evidence implies individual knowledge for each agent. Normally, the following monotonicity property is also assumed: 4) any piece of evidence is compatible with any other evidence. We show that the evidence-based knowledge operator is a stronger version of the common knowledge operator. Evidence-based knowledge is free of logical omniscience, model-independent, and has a natural motivation. Furthermore, evidence-based knowledge can be presented by normal multi-modal logics, which are in the scope of well-developed machinery applicable to modal logic: epistemic models, normalized proofs, automated proof search, etc.