Infinite States Verification in Game-Theoretic Logics: Case Studies and Implementation

Many practical problems where the environment is not in the system’s control can be modelled in game-theoretic logics (e.g., ATL). But most work on verification methods for such logics is restricted to finite state cases. De Giacomo, Lespérance, and Pearce have proposed a situation calculus-based logical framework for representing such infinite state game-type problems together with a verification method based on fixpoint approximates and regression. Here, we extend this line of work. Firstly, we describe some case studies to evaluate the method. We specify some example domains and show that the method does allow us to verify various properties. We also find some examples where the method must be extended to exploit information about the initial state and state constraints in order to work. Secondly, we describe an evaluation-based Prolog implementation of a version of the method for complete initial state theories with the closed world assumption. It generates successive approximates and checks if they hold in the situation of interest. We describe some preliminary experiments with this tool and discuss its limitations.