Complete Axiomatization and Complexity of 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. However CL can not formalize the evolvement of rational mental attitudes of the agents such as knowledge. 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 the coalitional forces and the temporal properties of strategic abilities as well. Furthermore, we provide a complete axiomatization of CLTK, along with the complexity of the satisfiability problem, which is shown to be EXPTIME-complete.