Model Checking Abilities under Incomplete Information Is Indeed Delta2-complete

We study the model checking complexity of Alternating-time temporal logic with imperfect information and imperfect recall (atlir). Contrary to what we have stated in [11], the problem turns out to be ∆2 -complete, thus con rming the initial intuition of Schobbens [18]. We prove ∆2 -hardness through a reduction of the SNSAT problem, while the membership in ∆ P 2 stems from the algorithm presented in [18].