{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T06:12:53Z","timestamp":1768457573364,"version":"3.49.0"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T00:00:00Z","timestamp":1632700800000},"content-version":"unspecified","delay-in-days":26,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints <jats:italic>\u00e0 la<\/jats:italic> IFF, possibly annotated with a probability value. We first present the overall abductive language and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.<\/jats:p>","DOI":"10.1017\/s1471068421000417","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T14:41:41Z","timestamp":1632753701000},"page":"557-574","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":7,"title":["Nonground Abductive Logic Programming with Probabilistic Integrity Constraints"],"prefix":"10.1017","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3717-3779","authenticated-orcid":false,"given":"ELENA","family":"BELLODI","sequence":"first","affiliation":[]},{"given":"MARCO","family":"GAVANELLI","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8352-6304","authenticated-orcid":false,"given":"RICCARDO","family":"ZESE","sequence":"additional","affiliation":[]},{"given":"EVELINA","family":"LAMMA","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1654-9703","authenticated-orcid":false,"given":"FABRIZIO","family":"RIGUZZI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,9,27]]},"reference":[{"key":"S1471068421000417_ref14","doi-asserted-by":"crossref","unstructured":"Kakas, A. , Kowalski, R. and Toni, F. 1998. The role of abduction in logic programming. In Handbook of Logic in Artificial Intelligence and Logic Programming. Vol 5. Oxford University Press, 235\u2013324.","DOI":"10.1093\/oso\/9780198537922.003.0007"},{"key":"S1471068421000417_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0743-1066(87)90007-0"},{"key":"S1471068421000417_ref20","unstructured":"Raghavan, S. V. 2011. Bayesian abductive logic programs: A probabilistic logic for abductive reasoning. In Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI-11). IJCAI\/AAAI, 2840\u20132841."},{"key":"S1471068421000417_ref24","doi-asserted-by":"crossref","unstructured":"Turliuc, C.-R. , Maimari, N. , Russo, A. and Broda, K. 2013. On minimality and integrity constraints in probabilistic abduction. In Logic for Programming, Artificial Intelligence, and Reasoning. 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