In another variant of PDL, due to Peleg [1987] and further studied by Goldblatt [1992b], the expression α∩β is interpreted “do α and β in parallel”. In this context, the binary relations R(α) and R(β) are no longer sets of pairs of the form (x,y) with x, y worlds, but rather sets of pairs of the form (x,Y) with x a world and Y a set of worlds. It was inspired by the Game Logic of Parikh [1985], an intepretation of PDL with “programs as games”. Game Logic provides an additional program construct that dualizes programs, thus permitting to define the intersection of programs as the dual of the non-deterministic choice between programs.