Proceedings

A Fine-Grained Complexity View on Propositional Abduction - Algorithms and Lower Bounds

Victor Lagerkvist, Mohamed Maizia, Johannes Schmidt

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Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence. Main Track. Pages 4562-4569.

https://doi.org/10.24963/ijcai.2025/508

Keywords

  • Constraint Satisfaction and Optimization: CSO: Constraint satisfaction
  • Knowledge Representation and Reasoning: KRR: Non-monotonic reasoning
  • Constraint Satisfaction and Optimization: CSO: Satisfiabilty
  • Knowledge Representation and Reasoning: KRR: Diagnosis and abductive reasoning

Abstract

The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning, e.g., abductive reasoning, comparably little is known outside classic complexity theory. In this paper we take a first step of bridging the gap between monotonic and non-monotonic reasoning by analyzing the complexity of intractable abduction problems under the seemingly overlooked but natural parameter n: the number of variables in the knowledge base. We obtain several positive results for SigmaP2- as well as NP- and coNP-complete fragments, which implies the first example of beating exhaustive search for a SigmaP2-complete problem (to the best of our knowledge). We complement this with lower bounds and for many fragments rule out improvements under the (strong) exponential-time hypothesis.

Victor Lagerkvist, Mohamed Maizia, and Johannes Schmidt. 2025. A Fine-Grained Complexity View on Propositional Abduction - Algorithms and Lower Bounds. In Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25. IJCAI, 4562–4569. https://doi.org/10.24963/ijcai.2025/508
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