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Logic Journal of IGPL 2005 13(1):5-28; doi:10.1093/jigpal/jzi002
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© The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

Reasoning about Knowledge in Asynchronous Distributed Systems

Vania Costa1 and Mario Benevides2

1 System Engineering and Computer Science Program – UFRJ – Mailbox 68511, zipcode 21945-970 Rio de Janeiro, Brazil. E-mail: vaniac{at}cos.ufrj.br, 2 System Engineering and Computer Science Program and Mathematics Institute – UFRJ – Mailbox 68511, zipcode 21945-970 Rio de Janeiro, Brazil. E-mail: mario{at}cos.ufrj.br

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.

Key Words: many-dimensional logics, multi-agent systems, epistemic logics

Received 16 December 2003. Revised version 8 October 2004.


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