A complete coalition logic of temporal knowledge for multi-agent systems

Abstract

Coalition logic (CL) is one of the most influential logical formalisms for strategic abilities of multi-agent systems. CL can specify what a group of agents can achieve through choices of their actions, denoted by [C]\varphi to state that a group of agents C can have a strategy to bring about \varphi by collective actions, no matter what the other agents do. However, CL lacks the temporal dimension and thus can not capture the dynamic aspects of a system. Therefore, CL can not formalize the evolvement of rational mental attitudes of the agents such as knowledge, which has been shown to be very useful in specifications and verifications of distributed systems, and has received substantial amount of studies. In this paper, we introduce coalition logic of temporal knowledge (CLTK), by incorporating a temporal logic of knowledge (Halpern and Vardi’s logic of CKL_n) into CL to equip CL with the power to formalize how agents’ knowledge (individual or group knowledge) evolves over the time by coalitional forces and the temporal properties of strategic abilities as well. Furthermore, we provide an axiomatic system for CLTK and prove that it is sound and complete, along with the complexity of the satisfiability problem which is shown to be EXPTIME-complete.

Keywords

coalition logic / temporal logic of knowledge / complete axiomatization / multi-agent systems

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