{"type":"ScholarlyArticle","title":"Optimality-preserving Logic-Based Benders Decomposition of Answer Set Programs","authors":[{"name":"Carmine Dodaro","slug":"carmine-dodaro","given":"Carmine","family":"Dodaro","affiliation":""},{"name":"Antonio Ielo","slug":"antonio-ielo","given":"Antonio","family":"Ielo","affiliation":""},{"name":"Marco Maratea","slug":"marco-maratea","given":"Marco","family":"Maratea","affiliation":""},{"name":"Cinzia Marte","slug":"cinzia-marte","given":"Cinzia","family":"Marte","affiliation":""},{"name":"Alice Tarzariol","slug":"alice-tarzariol","given":"Alice","family":"Tarzariol","affiliation":""}],"abstract":"Bender Decomposition is a well-known solving technique in Operation Research that decomposes a problem into a master and a subproblem, which interact via “cuts\". This technique has been extended to Logic-Based Bender Decomposition (LBBD), solving problems specified by logic-based languages and enabling a wider applicability. However, while Bender Decomposition guarantees optimality, LBBD does not: this property is problem-specific and depends on the defined decomposition and cuts.\r\nIn this paper, we present a theoretical analysis of the conditions under which LBBD, including cuts, can preserve optimality in the context of Answer Set Programming (ASP), a prominent logic-based language in the field of Artificial Intelligence.\r\nWe also introduce a general-purpose algorithm that employs both minimal unsatisfiable subsets and minimal correction subsets to define cuts in a fully automated, problem-independent way. The algorithm preserves the optimality guarantees of Bender Decomposition.\r\nAn empirical evaluation on real-world scheduling instances shows that our approach can find significantly more solutions, and more optimal ones, compared to a standard direct ASP encoding, while also consistently reducing the execution time.","doi":"10.24963/ijcai.2026/424","url":"https://ijcai.org/proceedings/2026/424","pdf":"https://ijcai.org/proceedings/2026/0424.pdf","markdown":"https://ijcai.org/proceedings/2026/424.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/424","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":424,"pages":{"first":3810,"last":3818},"keywords":["Knowledge Representation and Reasoning: Logic programming","Knowledge Representation and Reasoning: Non-monotonic reasoning"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}