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On the Size Complexity and Decidability of First-Order Progression

Jens Claßen, Daxin Liu

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Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence. Main Track. Pages 3801-3809.

https://doi.org/10.24963/ijcai.2026/423

Keywords

  • Knowledge Representation and Reasoning: Computational complexity of reasoning
  • Knowledge Representation and Reasoning: Reasoning about actions

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.

Jens Claßen, and Daxin Liu. 2026. On the Size Complexity and Decidability of First-Order Progression. In Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26. IJCAI, 3801–3809. https://doi.org/10.24963/ijcai.2026/423
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