Reasoning about knowledge in asynchronous distributed systems

This paper introduces a two-dimensional modal logic to reason about knowledge in asynchronous multi-agent message-passing systems. We present a new theoretical definition for concurrent knowledge in order to describe the kind of knowledge typical in such asynchronous environments. To define concurrent knowledge, we propose the closed sub-product of modal logics: a two-dimensional formal semantics where one dimension corresponds to asynchronous runs, the other corresponds to consistent cuts (or global states) and the concurrent knowledge is defined as the transitive closure over the product of the former dimensions. We axiomatize the presented logic issuing proofs of soundness and completeness with respect to the class of closed sub-product of modal frames.