{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T13:00:28Z","timestamp":1761310828587,"version":"build-2065373602"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2025,8,20]],"date-time":"2025-08-20T00:00:00Z","timestamp":1755648000000},"content-version":"unspecified","delay-in-days":50,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Probabilistic Logic Programming (PLP) under the distribution semantics is a leading approach to practical reasoning under uncertainty. An advantage of the distribution semantics is its suitability for implementation as a Prolog or Python library, available through two well-maintained implementations, namely ProbLog and cplint\/PITA. However, current formulations of the distribution semantics use point-probabilities, making it difficult to express epistemic uncertainty, such as arises from, for example, hierarchical classifications from computer vision models. Belief functions generalize probability measures as non-additive capacities and address epistemic uncertainty via interval probabilities. This paper introduces interval-based\n                    <jats:italic>Capacity Logic Programs<\/jats:italic>\n                    based on an extension of the distribution semantics to include belief functions and describes properties of the new framework that make it amenable to practical applications.\n                  <\/jats:p>","DOI":"10.1017\/s1471068425100161","type":"journal-article","created":{"date-parts":[[2025,8,20]],"date-time":"2025-08-20T07:26:34Z","timestamp":1755674794000},"page":"455-472","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Integrating Belief Domains into Probabilistic Logic Programs"],"prefix":"10.1017","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7133-2673","authenticated-orcid":false,"given":"DAMIANO","family":"AZZOLINI","sequence":"first","affiliation":[{"name":"University of Ferrara"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1654-9703","authenticated-orcid":false,"given":"FABRIZIO","family":"RIGUZZI","sequence":"additional","affiliation":[{"name":"University of Ferrara"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6446-0650","authenticated-orcid":false,"given":"THERESA","family":"SWIFT","sequence":"additional","affiliation":[{"name":"Johns Hopkins Applied Physics Lab"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,8,20]]},"reference":[{"key":"S1471068425100161_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(92)90048-3"},{"key":"S1471068425100161_ref8","first-page":"2462","volume-title":"20th International Joint Conference On Artificial Intelligence (IJCAI 2007)","volume":"7","author":"De Raedt","year":"2007"},{"key":"S1471068425100161_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-44797-0_10"},{"key":"S1471068425100161_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(00)00029-1"},{"key":"S1471068425100161_ref28","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-015-5488-x"},{"key":"S1471068425100161_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-38812-5_6"},{"key":"S1471068425100161_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-30690-2"},{"key":"S1471068425100161_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068408003645"},{"key":"S1471068425100161_ref17","unstructured":"Lee, J. and Yang, Z. 2017. LPMLN, weak constraints, and P-log. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, February 4-9, 2017, Singh, S. and Markovitch, S. , Eds. AAAI Press, 1170\u20131177."},{"key":"S1471068425100161_ref5","first-page":"517","volume-title":"19th International Conference on Uncertainty in Artificial Intelligence (UAI 2003)","author":"Costa","year":"2003"},{"key":"S1471068425100161_ref26","doi-asserted-by":"publisher","DOI":"10.1515\/9780691214696"},{"key":"S1471068425100161_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04238-6_27"},{"key":"S1471068425100161_ref7","doi-asserted-by":"publisher","DOI":"10.1613\/jair.5482"},{"key":"S1471068425100161_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068410000566"},{"key":"S1471068425100161_ref22","doi-asserted-by":"publisher","DOI":"10.1145\/73721.73723"},{"key":"S1471068425100161_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-42337-1"},{"key":"S1471068425100161_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/S0888-613X(00)00032-3"},{"volume-title":"Proc. of the 34th International Conference on Machine Learning, ICML 2017","year":"2017","author":"Guo","key":"S1471068425100161_ref12"},{"volume-title":"Probability and Measure Theory","year":"2000","author":"Ash","key":"S1471068425100161_ref1"},{"key":"S1471068425100161_ref9","first-page":"9662","volume-title":"Advances in Neural Information Processing Systems","volume":"33","author":"Giunchiglia","year":"2020"},{"key":"S1471068425100161_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(93)90061-F"},{"key":"S1471068425100161_ref24","doi-asserted-by":"publisher","DOI":"10.1017\/S147106841100010X"},{"key":"S1471068425100161_ref25","first-page":"715","volume-title":"ICLP\u201995: Proceedings of the 12th International Conference on Logic Programming","author":"Sato","year":"1995"},{"key":"S1471068425100161_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13840-9_10"},{"key":"S1471068425100161_ref4","doi-asserted-by":"publisher","DOI":"10.5802\/aif.53"},{"key":"S1471068425100161_ref3","doi-asserted-by":"publisher","DOI":"10.1145\/2043174.2043195"},{"key":"S1471068425100161_ref23","doi-asserted-by":"publisher","DOI":"10.1201\/9781003338192"},{"key":"S1471068425100161_ref19","first-page":"254","article-title":"Stochastic logic programs","volume":"32","author":"Muggleton","year":"1996","journal-title":"Advances in Inductive Logic Programming"},{"key":"S1471068425100161_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0743-1066(99)00071-0"}],"container-title":["Theory and Practice of Logic Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1471068425100161","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T12:56:33Z","timestamp":1761310593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068425100161\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["S1471068425100161"],"URL":"https:\/\/doi.org\/10.1017\/s1471068425100161","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"type":"print","value":"1471-0684"},{"type":"electronic","value":"1475-3081"}],"subject":[],"published":{"date-parts":[[2025,7]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}