Summary: Alternating-time Temporal Logic (ATL) is probably the most influential logic of strategic ability that has emerged in recent years. The idea of ATL is centered around cooperation modalities: \(\langle\langle A\rangle\rangle_\gamma\) is satisfied if the group \(A\) of agents has a collective strategy to enforce temporal property \(\gamma\) against the worst possible response from the other agents. So, the semantics of ATL shares the “all-or-nothing” attitude of many logical approaches to computation.
Such an assumption seems appropriate in some application areas (life-critical systems, security protocols, expensive ventures like space missions). In many cases, however, one might be satisfied if the goal is achieved with reasonable likelihood. In this paper, we try to soften the rigorous notion of success that underpins ATL.