Abstract:Progression, the task of updating a knowledge base to reflect action effects, generally requires second-order logic. Identifying first-order special cases, by restricting either the knowledge base or action effects, has long been a central topic in reasoning about actions. It is known that local-effect, normal, and acyclic actions, three increasingly expressive classes, admit first-order progression. However, a systematic analysis of the size of such progressions, crucial for practical applications, has been missing. In this paper, using the framework of Situation Calculus, we show that under reasonable assumptions, first-order progression for these action classes grows only polynomially. Moreover, we show that when the KB belongs to decidable fragments such as two-variable first-order logic or universal theories with constants, the progression remains within the same fragment, ensuring decidability and practical applicability.
| Comments: | This is an extended version of an identically-titled paper accepted for publication at IJCAI 2026. This version contains an appendix with further proofs |
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.12691 [cs.AI] |
| (or arXiv:2605.12691v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2605.12691 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jens Classen [view email]
[v1]
Tue, 12 May 2026 19:40:45 UTC (32 KB)