{"type":"ScholarlyArticle","title":"Quantitative Reasoning over Incomplete Abstract Argumentation Frameworks","authors":[{"name":"Bettina Fazzinga","slug":"bettina-fazzinga","given":"Bettina","family":"Fazzinga","affiliation":"DiCES -University of Calabria"},{"name":"Sergio Flesca","slug":"sergio-flesca","given":"Sergio","family":"Flesca","affiliation":"DIMES -University of Calabria"},{"name":"Filippo Furfaro","slug":"filippo-furfaro","given":"Filippo","family":"Furfaro","affiliation":"DIMES -University of Calabria"},{"name":"Giuseppina Monterosso","slug":"giuseppina-monterosso","given":"Giuseppina","family":"Monterosso","affiliation":"DIMES -University of Calabria"}],"abstract":"We introduce PERCVER and PERCACC, the problems asking for the percentages of the completions of an incomplete Abstract Argumentation Framework (iAAF)  where a set of arguments S is an extension and an argument a is accepted, respectively. These problems give insights into the status of S and a more precise than the “traditional” verification and acceptance tests under the possible and necessary perspectives, that decide if S is an extension and a is accepted in at least one or every completion, respectively. As a first contribution, we investigate the relationship between the proposed framework and probabilistic AAFs (prAAFs) under the constellations approach (that, at first sight, seem to be suitable for starightforwardly encoding the quantitative reasoning underlying PERCVER and PERCACC). In this regard, we show that translating an iAAF into an equivalent prAAF requires a heavy computational cost: this backs the study of PERCVER and PERCACC as new distinguished problems. Then, we investigate the complexity of PERCVER and PERCACC, and we identify interesting islands of tractability.","doi":"10.24963/ijcai.2024/372","url":"https://ijcai.org/proceedings/2024/372","pdf":"https://ijcai.org/proceedings/2024/0372.pdf","markdown":"https://ijcai.org/proceedings/2024/372.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/372","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":372,"pages":{"first":3360,"last":3368},"keywords":["Knowledge Representation and Reasoning: KRR: Argumentation","Knowledge Representation and Reasoning: KRR: Computational complexity of reasoning"],"videos":[],"references":[{"position":1,"raw":"[Alfano et al., 2023a] Gianvincenzo Alfano, Marco Calautti, Sergio Greco, Francesco Parisi, and Irina Trubitsyna. 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