Robust Alternating-Time Temporal Logic

Abstract: 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*.