{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T22:00:42Z","timestamp":1747173642848,"version":"3.40.5"},"reference-count":45,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2019,1,14]],"date-time":"2019-01-14T00:00:00Z","timestamp":1547424000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2019,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>When modeling real-world domains, we have to deal with information that is incomplete or that comes from sources with different trust levels. This motivates the need for managing uncertainty in the Semantic Web. To this purpose, we introduced a probabilistic semantics, named DISPONTE, in order to combine description logics (DLs) with probability theory. The probability of a query can be then computed from the set of its explanations by building a Binary Decision Diagram (BDD). The set of explanations can be found using the<jats:italic>tableau algorithm<\/jats:italic>, which has to handle non-determinism. Prolog, with its efficient handling of non-determinism, is suitable for implementing the tableau algorithm. TRILL and TRILL<jats:italic><jats:sup>P<\/jats:sup><\/jats:italic>are systems offering a Prolog implementation of the tableau algorithm. TRILL<jats:italic><jats:sup>P<\/jats:sup><\/jats:italic>builds a<jats:italic>pinpointing formula<\/jats:italic>that compactly represents the set of explanations and can be directly translated into a BDD. Both reasoners were shown to outperform state-of-the-art DL reasoners. In this paper, we present an improvement of TRILL<jats:italic><jats:sup>P<\/jats:sup><\/jats:italic>, named TORNADO, in which the BDD is directly built during the construction of the tableau, further speeding up the overall inference process. An experimental comparison shows the effectiveness of TORNADO. All systems can be tried online in the TRILL on SWISH web application at<jats:uri xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:type=\"simple\" xlink:href=\"http:\/\/trill.ml.unife.it\/\">http:\/\/trill.ml.unife.it\/<\/jats:uri>.<\/jats:p>","DOI":"10.1017\/s1471068418000480","type":"journal-article","created":{"date-parts":[[2019,1,14]],"date-time":"2019-01-14T04:46:12Z","timestamp":1547441172000},"page":"449-476","source":"Crossref","is-referenced-by-count":3,"title":["Probabilistic DL Reasoning with Pinpointing Formulas: A Prolog-based Approach"],"prefix":"10.1017","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8352-6304","authenticated-orcid":false,"given":"RICCARDO","family":"ZESE","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GIUSEPPE","family":"COTA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EVELINA","family":"LAMMA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ELENA","family":"BELLODI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1654-9703","authenticated-orcid":false,"given":"FABRIZIO","family":"RIGUZZI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2019,1,14]]},"reference":[{"key":"S1471068418000480_ref45","doi-asserted-by":"publisher","DOI":"10.1007\/s10472-016-9529-3"},{"key":"S1471068418000480_ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.websem.2007.03.004"},{"key":"S1471068418000480_ref39","first-page":"715","volume-title":"Logic Programming, Proc. of the 12th International Conference on Logic Programming","author":"Sato","year":"1995"},{"key":"S1471068418000480_ref38","doi-asserted-by":"publisher","DOI":"10.1017\/S147106841100010X"},{"key":"S1471068418000480_ref43","first-page":"292","volume-title":"Proc. of the Automated Reasoning, 3rd International Joint Conference, IJCAR 2006","volume":"4130","author":"Tsarkov","year":"2006"},{"key":"S1471068418000480_ref37","first-page":"162","volume-title":"Technical Communications of the 26th International Conference on Logic Programming, ICLP 2010","volume":"7","author":"Riguzzi","year":"2010"},{"volume-title":"The Semantic Web - ISWC 2003, 2nd International Semantic Web Conference","year":"2003","author":"Patel-Schneider","key":"S1471068418000480_ref32"},{"key":"S1471068418000480_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2007.10.017"},{"key":"S1471068418000480_ref44","volume-title":"Probabilistic Semantic Web: Reasoning and Learning","volume":"28","author":"Zese","year":"2017"},{"key":"S1471068418000480_ref31","first-page":"74","volume-title":"Proceedings of the 1995 IEEE\/ACM International Conference on Computer-Aided Design, ICCAD 1995","author":"Panda","year":"1995"},{"key":"S1471068418000480_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(86)90031-7"},{"key":"S1471068418000480_ref29","first-page":"393","volume-title":"12th International Conference on Principles of Knowledge Representation and Reasoning (KR 2010)","author":"Lutz","year":"2010"},{"key":"S1471068418000480_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s10817-010-9181-2"},{"key":"S1471068418000480_ref27","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068409003792"},{"key":"S1471068418000480_ref36","doi-asserted-by":"publisher","DOI":"10.3233\/SW-140154"},{"key":"S1471068418000480_ref26","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068400001058"},{"key":"S1471068418000480_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-68234-9_66"},{"key":"S1471068418000480_ref24","first-page":"354","volume-title":"CADE","volume":"6803","author":"Klinov","year":"2011"},{"key":"S1471068418000480_ref9","first-page":"1","volume-title":"Uncertainty Reasoning for the Semantic Web II, International Workshops URSW 2008\u20132010 Held at ISWC and UniDL 2010 Held at FLoC, Revised Selected Papers","volume":"7123","author":"Carvalho","year":"2013"},{"key":"S1471068418000480_ref33","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(87)90062-2"},{"key":"S1471068418000480_ref7","unstructured":"Bock, C. , Fokoue, A. , Hoekstra, R. , Horrocks, I. , Ruttenberg, A. , Sattler, U. and Smith, M. 2012. 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