Dealing with imperfect information in Strategy Logic

We propose an extension of Strategy Logic (SL), in which one can both reason about strategizing under imperfect information and about players’ knowledge. One original aspect of our approach is that we do not force strategies to be uniform, i.e. consistent with the players’ information, at the semantic level; instead, one can express in the logic itself that a strategy should be uniform. To do so, we first develop a “branching-time” version of SL with perfect information, that we call BSL, in which one can quantify over the different outcomes defined by a partial assignment of strategies to the players; this contrasts with SL, where temporal operators are allowed only when all strategies are fixed, leaving only one possible play. Next, we further extend BSL by adding distributed knowledge operators, the semantics of which rely on equivalence relations on partial plays. The logic we obtain subsumes most strategic logics with imperfect information, epistemic or not.