In multi-agent system design, a crucial aspect is to ensure robustness, meaning that for a coalition of agents A, small violations of adversarial assumptions only lead to small violations of A's goals. In this paper we introduce a logical framework for robust strategic reasoning about multi-agent systems. Specifically, inspired by recent works on robust temporal logics, we introduce and study rATL and rATL*, logics that extend the well-known Alternating-time Temporal Logic ATL and ATL* by means of an opportune multi-valued semantics for the strategy quantifiers and temporal operators. We study the model-checking and satisfiability problems for rATL and rATL* and show that dealing with robustness comes at no additional computational cost. Indeed, we show that these problems are PTime-complete and ExpTime-complete for rATL, respectively, while both are 2ExpTime-complete for rATL*.

翻译：在多智能体系统设计中，一个关键方面是确保鲁棒性，即对于智能体联盟A而言，对抗性假设的微小偏离仅会导致A目标的微小偏离。本文提出了一种用于多智能体系统鲁棒策略推理的逻辑框架。具体而言，受近期关于鲁棒时态逻辑研究的启发，我们引入并研究了rATL与rATL*——这两种逻辑通过为策略量词和时态算子赋予适当的多值语义，扩展了经典的交替时态逻辑ATL和ATL*。我们研究了rATL与rATL*的模型检测与可满足性问题，并表明处理鲁棒性不会带来额外的计算代价。实际上，我们证明这些问题对rATL而言分别为PTime完备和ExpTime完备，而对rATL*则均为2ExpTime完备。