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arXiv · 2412.11217

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
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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.

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Liangda Fang, Xiaoman Wang, Zhang Chen, Kailun Luo, Zhenhe Cui, Quanlong Guan. 2024-12-15. A Syntactic Approach to Computing Complete and Sound Abstraction in the Situation Calculus. https://arxiv.org/abs/2412.11217

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