Decidable Verification of Golog Programs over Non-Local Effect Actions: Extended Version

The Golog action programming language is a powerful means to express high-level behaviours in terms of programs over actions defined in a Situation Calculus theory. In particular for physical systems, verifying that the 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 and program constructs. So far, approaches to achieve decidability involved restrictions where action effects either had to be contextfree (i.e. not depend on the current state), local (i.e. only affect objects mentioned in the action’s parameters), or at least bounded (i.e. only affect a finite number of objects). In this paper, we present a new, more general class of action theories (called acyclic) that allows for context-sensitive, non-local, unbounded effects, i.e. actions that may affect an unbounded number of possibly unnamed objects in a state-dependent fashion. We contribute to the further exploration of the boundary between decidability and undecidability for Golog, showing that for acyclic theories in the two-variable fragment of first-order logic, verification of CTL properties of programs over ground actions is decidable

Exploring the Boundaries of Decidable Verification of Non-Terminating Golog Programs

The action programming language GOLOG has been found useful for the control of autonomous agents such as mobile robots. In scenarios like these, tasks are often open-ended so that the respective control programs are non-terminating. Before deploying such programs on a robot, it is often desirable to verify that they meet cer-tain requirements. For this purpose, Claßen and Lake-meyer recently introduced algorithms for the verifica-tion of temporal properties of GOLOG programs. How-ever, given the expressiveness of GOLOG, their verifi-cation procedures are not guaranteed to terminate. In this paper, we show how decidability can be obtained by suitably restricting the underlying base logic, the ef-fect axioms for primitive actions, and the use of actions within GOLOG programs. Moreover, we show that drop-ping any of these restrictions immediately leads to un-decidability of the verification problem