{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T01:30:01Z","timestamp":1785202201833,"version":"3.55.0"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"5-6","license":[{"start":{"date-parts":[[2017,9,4]],"date-time":"2017-09-04T00:00:00Z","timestamp":1504483200000},"content-version":"unspecified","delay-in-days":3,"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":[[2017,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Hybrid MKNF knowledge bases have been considered one of the dominant approaches to combining open world ontology languages with closed world rule-based languages. Currently, the only known inference methods are based on the approach of guess-and-verify, while most modern SAT\/ASP solvers are built under the DPLL architecture. The central impediment here is that it is not clear what constitutes a constraint propagator, a key component employed in any DPLL-based solver. In this paper, we address this problem by formulating the notion of unfounded sets for non-disjunctive hybrid MKNF knowledge bases, based on which we propose and study two new well-founded operators. We show that by employing a well-founded operator as a constraint propagator, a sound and complete DPLL search engine can be readily defined. We compare our approach with the operator based on the alternating fixpoint construction by Knorr <jats:italic>et al.<\/jats:italic> (2011. <jats:italic>Artificial Intelligence 175<\/jats:italic>, 9, 1528\u20131554) and show that, when applied to arbitrary partial partitions, the new well-founded operators not only propagate more truth values but also circumvent the non-converging behavior of the latter. In addition, we study the possibility of simplifying a given hybrid MKNF knowledge base by employing a well-founded operator and show that, out of the two operators proposed in this paper, the weaker one can be applied for this purpose and the stronger one cannot. These observations are useful in implementing a grounder for hybrid MKNF knowledge bases, which can be applied before the computation of MKNF models.<\/jats:p>","DOI":"10.1017\/s1471068417000291","type":"journal-article","created":{"date-parts":[[2017,9,4]],"date-time":"2017-09-04T09:31:18Z","timestamp":1504517478000},"page":"889-905","source":"Crossref","is-referenced-by-count":4,"title":["Well-founded operators for normal hybrid MKNF knowledge bases"],"prefix":"10.1017","volume":"17","author":[{"given":"JIANMIN","family":"JI","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"FANGFANG","family":"LIU","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"JIA-HUAI","family":"YOU","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2017,9,4]]},"reference":[{"key":"S1471068417000291_ref10","first-page":"123","article-title":"Owl 2 web ontology language primer","volume":"27","author":"Hitzler","year":"2009","journal-title":"W3C Recommendation"},{"key":"S1471068417000291_ref9","unstructured":"Heule M. and Schaub T. 2015. What's hot in the SAT and ASP competitions. In Proc. of the 29th AAAI Conference on Artificial Intelligence (AAAI-15), 4322\u20134323."},{"key":"S1471068417000291_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2011.01.007"},{"key":"S1471068417000291_ref17","doi-asserted-by":"publisher","DOI":"10.1145\/1217856.1217859"},{"key":"S1471068417000291_ref1","first-page":"487","article-title":"Unfounded sets and well-founded semantics of answer set programs with aggregates","volume":"42","author":"Alviano","year":"2011","journal-title":"Journal of Artificial Intelligence Research"},{"key":"S1471068417000291_ref14","unstructured":"Lifschitz V. 1991. Nonmonotonic databases and epistemic queries. In Proc. of the 12th International Joint Conference on Artificial Intelligence (IJCAI-91), 381\u2013386."},{"key":"S1471068417000291_ref16","doi-asserted-by":"publisher","DOI":"10.1145\/1754399.1754403"},{"key":"S1471068417000291_ref11","unstructured":"Ji J. , Wan H. , Huo Z. and Yuan Z. 2015. Simplifying A logic program using its consequences. In Proc. of the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015), July 25\u201331, 2015, Buenos Aires, Argentina, 3069\u20133075."},{"key":"S1471068417000291_ref15","doi-asserted-by":"publisher","DOI":"10.1145\/1536616.1536637"},{"key":"S1471068417000291_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s10472-010-9207-9"},{"key":"S1471068417000291_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(93)90024-Q"},{"key":"S1471068417000291_ref20","doi-asserted-by":"publisher","DOI":"10.1145\/116825.116838"},{"key":"S1471068417000291_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(02)00187-X"},{"key":"S1471068417000291_ref13","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1997.2630"},{"key":"S1471068417000291_ref2","volume-title":"The Description Logic Handbook: Theory, Implementation, and Applications","author":"Baader","year":"2003"},{"key":"S1471068417000291_ref22","unstructured":"Zhang L. and Malik S. 2002. The quest for efficient Boolean satisfiability solvers. In Proc. of the14th International Conference on Computer Aided Verification, (CAV 2002), July 27\u201331, 2002, Copenhagen, Denmark, 17\u201336."},{"key":"S1471068417000291_ref6","unstructured":"Eiter T. , Kaminski T. , Redl C. and Weinzierl A. 2016. Exploiting partial assignments for efficient evaluation of answer set programs with external source access. In Proc. of the 25th International Joint Conference on Artificial Intelligence (IJCAI 2016), New York, NY, USA, 9\u201315 July 2016, 1058\u20131065."},{"key":"S1471068417000291_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2012.04.001"},{"key":"S1471068417000291_ref19","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1955.5.285"},{"key":"S1471068417000291_ref4","doi-asserted-by":"crossref","unstructured":"Bi Y. , You J. and Feng Z. 2014. A generalization of approximation fixpoint theory and application. In Proc. of the 8th International Conference on Web Reasoning and Rule Systems, 45\u201359.","DOI":"10.1007\/978-3-319-11113-1_4"},{"key":"S1471068417000291_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543357"},{"key":"S1471068417000291_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2004.02.004"}],"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\/S1471068417000291","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T01:51:35Z","timestamp":1555465895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068417000291\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9]]},"references-count":22,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["S1471068417000291"],"URL":"https:\/\/doi.org\/10.1017\/s1471068417000291","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9]]}}}