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

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, so as 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.