Bounded Situation Calculus Action Theories

TL;DR

This paper studies bounded action theories in the situation calculus, demonstrating that verifying a first-order mu-calculus variant is decidable for such theories, enabling checks on boundedness preservation.

Contribution

It introduces the concept of bounded action theories, analyzes their properties, and proves the decidability of verifying a powerful mu-calculus variant within this framework.

Findings

Verification of the mu-calculus variant is decidable for bounded theories.

Bounded theories are common due to facts not persisting or being forgotten.

Verification can determine if an action theory maintains boundedness.

Abstract

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.