A Syntactic Approach to Computing Complete and Sound Abstraction in the Situation Calculus
Liangda Fang, Xiaoman Wang, Zhang Chen, Kailun Luo, Zhenhe Cui, Quanlong Guan
TL;DR
This work addresses the challenge of computing complete and sound abstractions for reasoning about actions by introducing a LIBAT framework—a linear-integer version of the situation calculus—and extending an abstraction framework to EXT. It defines a restricted, syntactic refinement mapping from high-level to low-level theories, using guarded actions and forgetting to bridge the gap between theories. The main result provides a constructive procedure to derive high-level initial knowledge, action preconditions, and successor state axioms from a low-level theory under a set of stability and definability conditions, via a translation m^{-1} and m-bisimulation. The approach enables theory-level abstraction without exhaustive model checking, with potential impact on planning, verification, and generalized reasoning across domains. The authors also discuss future work to implement the method, automate refinement mappings, and relax restrictions for broader applicability.
Abstract
Abstraction is an important and useful concept in the field of artificial intelligence. To the best of our knowledge, there is no syntactic method to compute a sound and complete abstraction from a given low-level basic action theory and a refinement mapping. This paper aims to address this issue.To this end, we first present a variant of situation calculus,namely linear integer situation calculus, which serves as the formalization of high-level basic action theory. We then migrate Banihashemi, De Giacomo, and Lespérance's abstraction framework to one from linear integer situation calculus to extended situation calculus. Furthermore, we identify a class of Golog programs, namely guarded actions,that is used to restrict low-level Golog programs, and impose some restrictions on refinement mappings. Finally, we design a syntactic approach to computing a sound and complete abstraction from a low-level basic action theory and a restricted refinement mapping.