Decidable Verification of Decision-Theoretic Golog.

The Golog agent programming language is a powerful means to express high-level behaviours in terms of programs over actions defined in a Situation Calculus theory. Its variant DTGolog includes decision-theoretic aspects in the form of stochastic (probabilistic) actions and reward functions. In particular for physical systems such as robots, verifying that a program satisfies certain desired temporal properties is often crucial, but undecidable in general, the latter being due to the language's high expressiveness in terms of first-order quantification, range of action effects, and program constructs. Recent results for classical Golog show that by suitably restricting these aspects, the verification problem becomes decidable for a non-trivial fragment that retains a large degree of expressiveness. In this paper, we lift these results to the decision-theoretic case by providing an abstraction mechanism for reducing the infinite-state Markov Decision Process induced by the DTGolog program to a finite-state representation, which then can be fed into a state-of-the-art probabilistic model checker.