Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SL ii and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, problem is undecidable; but we a syntactical class “hierarchical instances” which, intuitively, as one goes down syntactic tree formula, strategy quantifications are concerned finer observations model, prove that restricted to hierarchical instances decidable. This result, because it allows complex patterns existential universal quantification on strategies, greatly generalises decidability distributed synthesis systems information. It us easily derive new results concerning strategic problems under information such existence Nash equilibria or rational synthesis. To establish go through intermediary, “low-level” much more adapted automata techniques. QCTL * CTL second-order over atomic propositions has been used logics perfect extend setting by parameterising quantifiers observations. The simple syntax resulting logic, , provide conceptually neat reduction separates concerns, allowing forget about strategies players focus solely quantification. While is, in general, undecidable, identify fragment formulas prove, using automata-theoretic approach,