{"type":"ScholarlyArticle","title":"Finite Groundings for ASP with Functions: A Journey through Consistency","authors":[{"name":"Lukas Gerlach","slug":"lukas-gerlach","given":"Lukas","family":"Gerlach","affiliation":"Knowledge-Based Systems Group , TU Dresden , Dresden , Germany"},{"name":"David Carral","slug":"david-carral","given":"David","family":"Carral","affiliation":"LIRMM , Inria , University of Montpellier , CNRS , Montpellier , France"},{"name":"Markus Hecher","slug":"markus-hecher","given":"Markus","family":"Hecher","affiliation":"Massachusetts Institute of Technology , United States"}],"abstract":"Answer set programming (ASP) is a logic programming formalism used in various areas of artificial intelligence like combinatorial problem solving and knowledge representation and reasoning. It is known that enhancing ASP with function symbols makes basic reasoning problems highly undecidable. However, even in simple cases, state of the art reasoners, specifically those relying on a ground-and-solve approach, fail to produce a result. Therefore, we reconsider consistency as a basic reasoning problem for ASP. We show reductions that give an intuition for the high level of undecidability. These insights allow for a more fine-grained analysis where we characterize ASP programs as \"frugal\" and \"non-proliferous\". For such programs, we are not only able to semi-decide consistency but we also propose a grounding procedure that yields finite groundings on more ASP programs with the concept of \"forbidden\" facts.","doi":"10.24963/ijcai.2024/375","url":"https://ijcai.org/proceedings/2024/375","pdf":"https://ijcai.org/proceedings/2024/0375.pdf","markdown":"https://ijcai.org/proceedings/2024/375.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/375","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":375,"pages":{"first":3386,"last":3394},"keywords":["Knowledge Representation and Reasoning: KRR: Knowledge representation languages","Knowledge Representation and Reasoning: KRR: Computational complexity of reasoning","Knowledge Representation and Reasoning: KRR: Logic programming","Knowledge Representation and Reasoning: KRR: Non-monotonic reasoning"],"videos":[],"references":[{"position":1,"raw":"[Alviano et al., 2010] Mario Alviano, Wolfgang Faber, Nicola Leone, Simona Perri, Gerald Pfeifer, and Giorgio Terracina. 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