A Modal Logic for Joint Abilities of Structured Strategies with Bounded Complexity

Ruiqi Jin, Yongmei Liu, Liping Xiong

Abstract: Coordination and joint ability are important topics in representation and reasoning about multi-agent systems. The modal logic JAADL proposed by Liu et al. extends ATL with joint abilities, which enables reasoning about whether a coalition of agents can coordinate and achieve a goal without communication. However, like ATL, strategic abilities in JAADL are defined in terms of combinatorial strategies, which are functions from histories or states to actions. On the other hand, there has been research on reasoning about natural strategic abilities, where a natural strategy is formalized as a sequence of condition-action pairs, making it more human-friendly than combinatorial strategy. In this work, we propose SJAADL, a variation of JAADL where strategic abilities are defined in terms of structured strategies represented with LDL (linear dynamic logic) formulas, with bounded complexity. We use nondeterministic strategies since they are more expressive, natural and succinct than determinstic ones. We present syntax and semantics of SJAADL. We show that model checking SJAADL can be done in time quasi-polynomial with the model size, exponential with the formula size, and with the complexity bound of structured strategies, exponential in the memoryless case and double exponential in the memoryful case. Finally, we introduce the problem of synthesizing norms to achieve joint abilities, and give two algorithms for it.