{"type":"ScholarlyArticle","title":"A Fine-Grained Complexity View on Propositional Abduction - Algorithms and Lower Bounds","authors":[{"name":"Victor Lagerkvist","slug":"victor-lagerkvist","given":"Victor","family":"Lagerkvist","affiliation":""},{"name":"Mohamed Maizia","slug":"mohamed-maizia","given":"Mohamed","family":"Maizia","affiliation":""},{"name":"Johannes Schmidt","slug":"johannes-schmidt","given":"Johannes","family":"Schmidt","affiliation":""}],"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.","doi":"10.24963/ijcai.2025/508","url":"https://ijcai.org/proceedings/2025/508","pdf":"https://ijcai.org/proceedings/2025/0508.pdf","markdown":"https://ijcai.org/proceedings/2025/508.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/508","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":508,"pages":{"first":4562,"last":4569},"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"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}