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 Lesperance’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.
BibTeX
@article{Fang_Wang_Chen_Luo_Cui_Guan_2025, title={A Syntactic Approach to Computing Complete and Sound Abstraction in the Situation Calculus}, volume={39}, url={https://ojs.aaai.org/index.php/AAAI/article/view/33635}, DOI={10.1609/aaai.v39i14.33635}, abstractNote={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 Lesperance’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.}, number={14}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Fang, Liangda and Wang, Xiaoman and Chen, Zhang and Luo, Kailun and Cui, Zhenhe and Guan, Quanlong}, year={2025}, month={Apr.}, pages={14911-14921} }