A Syntactic Approach to Computing Complete and Sound Abstraction in the Situation Calculus

TL;DR

This paper introduces a syntactic method for deriving sound and complete abstractions in the situation calculus, utilizing a new formalization and restrictions on Golog programs to improve high-level reasoning in AI.

Contribution

It presents a novel syntactic approach for abstraction in situation calculus, including a new formalization and restrictions on programs to ensure soundness and completeness.

Findings

Developed a variant of situation calculus called linear integer situation calculus.

Extended the abstraction framework to the extended situation calculus.

Designed a syntactic method to compute sound and complete abstractions.

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 Lesp\'erance'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.