On the Size Complexity and Decidability of First-Order Progression
This paper analyzes progression, a key task in reasoning about actions that updates a knowledge base to reflect action effects. Progression generally requires second-order logic, but first-order special cases exist for local-effect, normal, and acyclic actions. Using the Situation Calculus framework, the authors show that under reasonable assumptions, first-order progression for these classes grows only polynomially. Additionally, when the knowledge base belongs to decidable fragments such as two-variable first-order logic or universal theories with constants, progression remains within the same fragment, ensuring decidability and practical applicability.
[2605.12691] On the Size Complexity and Decidability of First-Order Progression
[Submitted on 12 May 2026]
Title:On the Size Complexity and Decidability of First-Order Progression
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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)
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