A stochastic interpretation of game logic

Game logic is a dynamic modal logic which models strategic two person games; it contains propositional dynamic logic (PDL) as a fragment. We propose an interpretation of game logic based on stochastic effectivity functions. A definition of these functions is given, and some algebraic properties of effectivity functions such as congruences are investigated. The relationship with stochastic relations is characterized through a deduction system. Logical and behavioral equivalence of game models is investigated. Finally the completion of models receives some attention.