Bounded Situation Calculus Action Theories
This addresses the need for automated verification in AI planning and reasoning, particularly for applications where facts are bounded due to persistence limits or forgetting, but it is incremental as it builds on existing situation calculus frameworks.
The paper tackles the problem of verifying action theories in the situation calculus where the number of object tuples in fluents is bounded by a constant across situations, showing that verification of a first-order mu-calculus variant is decidable for such theories.
In this paper, we investigate bounded action theories in the situation calculus. A bounded action theory is one which entails that, in every situation, the number of object tuples in the extension of fluents is bounded by a given constant, although such extensions are in general different across the infinitely many situations. We argue that such theories are common in applications, either because facts do not persist indefinitely or because the agent eventually forgets some facts, as new ones are learnt. We discuss various classes of bounded action theories. Then we show that verification of a powerful first-order variant of the mu-calculus is decidable for such theories. Notably, this variant supports a controlled form of quantification across situations. We also show that through verification, we can actually check whether an arbitrary action theory maintains boundedness.