{"type":"ScholarlyArticle","title":"Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics","authors":[{"name":"Pascal Kettmann","slug":"pascal-kettmann","given":"Pascal","family":"Kettmann","affiliation":""},{"name":"Jesse Heyninck","slug":"jesse-heyninck","given":"Jesse","family":"Heyninck","affiliation":""},{"name":"Hannes Strass","slug":"hannes-strass","given":"Hannes","family":"Strass","affiliation":""}],"abstract":"Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of the most prominent classical semantics, namely the stable model and the well-founded semantics, can be reconstructed within the general framework of approximation fixpoint theory (AFT).\r\n\r\nThis not only widens the scope of AFT from two- to many-valued logics, but allows a wide range of existing AFT results to be applied to fuzzy logic programming. As first examples of such applications, we clarify the formal relationship between existing semantics, generalize the notion of stratification from classical to fuzzy logic programs, and devise “more precise” variants of the semantics.","doi":"10.24963/ijcai.2025/506","url":"https://ijcai.org/proceedings/2025/506","pdf":"https://ijcai.org/proceedings/2025/0506.pdf","markdown":"https://ijcai.org/proceedings/2025/506.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/506","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":506,"pages":{"first":4544,"last":4552},"keywords":["Uncertainty in AI: UAI: Uncertainty representations","Knowledge Representation and Reasoning: KRR: Logic programming","Knowledge Representation and Reasoning: KRR: Non-monotonic reasoning"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}