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Reasoning about actions with loops via Hoare logic

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Abstract

Plans with loops are more general and compact than classical sequential plans, and gaining increasing attentions in artificial intelligence (AI). While many existing approaches mainly focus on algorithmic issues, few work has been devoted to the semantic foundations on planning with loops. In this paper, we first develop a tailored action language AL K, together with two semantics for handling domains with non-deterministic actions and loops. Then we propose a sound and (relative) complete Hoare-style proof system for efficient plan generation and verification under 0-approximation semantics, which uses the so-called idea offline planning and on-line querying strategy in knowledge compilation, i.e., the agent could generate and store short proofs as many as possible in the spare time, and then perform quick query by constructing a long proof from the stored shorter proofs using compositional rule. We argue that both our semantics and proof system could serve as logical foundations for reasoning about actions with loops.

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Authors and Affiliations

  1. Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou, 512075, China

    Jiankun He & Xishun Zhao

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  1. Jiankun He
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  2. Xishun Zhao
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Correspondence to Xishun Zhao.

Additional information

Jiankun He is currently a PhD student at the Institute of Logic and Cognition, Sun Yatsen University, China. His main research interests include knowledge representation and reasoning, formal semantics and methods in program verification.

Xishun Zhao is a professor at the Institute of Logic and Cognition, Sun Yat-sen University, China. He received his PhD degree in mathematics from Nanjing University, China in 1999. His current research interests include computational complexity in logic and analysis, knowledge representation and reasoning, expressive power and complexity of logic systems.

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He, J., Zhao, X. Reasoning about actions with loops via Hoare logic. Front. Comput. Sci. 10, 870–888 (2016). https://doi.org/10.1007/s11704-016-5158-6

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