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Strategy Reasoning in the Multi-agent Systems

Recently, the popular logical frameworks on strategy specification and verification in the multi-agent concurrent systems, such as alternating-time temporal logic and Strategy Logic (SL), mainly focus on the strategic abilities of one coalition. In them, the notion of strategy is just viewed as a pure syntax and/or semantics object, we cannot represent or reason about the internal structures of strategies, let alone strategic abilities under these ones. In this paper, based on linear dynamic logic, by extending SL, we propose a new strategic logic, named Dynamic Strategy Logic (DSL), which includes the existential/ universal quantification operators about regular expressions with test expressions. By introducing action atoms, we can specify both the evolution of time and structured strategies by means of regular expressions. Hence, in this logic, we can represent and reason about much more expressive strategic abilities under structured strategies of coalitions, and prove that DSL is more expressive than SL.