Towards a Probabilistic Interpretation of Game Logic

Game logic is a modal logic the modalities of which model the interaction of two players, Angel and Demon. It is known that game logic is not adequately interpreted through relation based Kripke models. The basic mechanism behind neighborhood models, which are used instead, is given through effectivity functions. We give a brief introduction to effectivity functions based on sets, indicate some of their coalgebraic properties, and move on to a definition of stochastic effectivity functions over general measurable spaces. An interpretation of game logics in terms of these effectivity functions is sketched, and their relationship to probabilistic Kripke models and to the interpretation of the PDL fragment is indicated.