A Temporal Logic for the Interaction of Strategies

Abstract

We propose an extension to ATL (alternating-time logic), called BSIL (basic strategy-interaction logic), for the specification of interaction among the strategies of agents in a multi-agent system. BSIL allows for the specifications of one system strategy that can cooperate with several strategies of the environment for different requirements. We argue that such properties are important in practice and rigorously show that such properties are not expressible in ATL ^*, GL (game logic), and AMC (alternating μ-calculus). Specifically, we show that BSIL is more expressive than ATL but incomparable with ATL^*, GL, and AMC in expressiveness. We show that a memoryful strategy is necessary for fulfilling a specification in BSIL. We also show that the model-checking problem of BSIL is PSPACE-complete and is of lower complexity than those of ATL^*, GL, AMC, and the general strategy logics. This may imply that BSIL can be useful in closing the gap between real-world projects and the game-theoretical results. We then show the plausibility and feasibility of our techniques by reporting our implementation and experiment with our PSPACE model-checking algorithm for BSIL. Finally, we discuss an extension of BSIL.

The work is partially supported by NSC (Grant NSC 97-2221-E-002-129-MY3, Taiwan, ROC) and by Research Center for Information Technology Innovation, Academia Sinica, Taiwan, ROC.

The authors would like to thank Prof. Moshe Vardi for his valuable suggestions.

A full version of the work with all the lemma proofs can be found in http://cc.ee.ntu.edu.tw/~farn.