@article(headcycleisNP, author = {Ben{-}Eliyahu, Rachel and Rina Dechter}, year = {1994}, title = {Propositional Semantics for Disjunctive Logic Programs}, journal = {Ann. Math. Artif. Intell.}, volume = {12}, number = {1-2}, pages = {53--87}, doi = {10.1007/BF01530761}, ) @incollection(denecker2000approximations, author = {Marc Denecker and Victor Marek and Miros{\l}aw Truszczy{\'n}ski}, year = {2000}, title = {Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning}, booktitle = {Logic-Based Artificial Intelligence}, publisher = {Springer}, pages = {127--144}, doi = {10.1007/978-1-4615-1567-8_6}, ) @article(DeneckerMT04, author = {Marc Denecker and Victor W. Marek and Miroslaw Truszczynski}, year = {2004}, title = {Ultimate approximation and its application in nonmonotonic knowledge representation systems}, journal = {Inf. Comput.}, volume = {192}, number = {1}, pages = {84--121}, doi = {10.1016/j.ic.2004.02.004}, ) @article(Fitting02, author = {Melvin Fitting}, year = {2002}, title = {Fixpoint semantics for logic programming a survey}, journal = {Theor. Comput. Sci.}, volume = {278}, number = {1-2}, pages = {25--51}, doi = {10.1016/S0304-3975(00)00330-3}, ) @article(gebserconflictdriven2012, author = {Martin Gebser and Benjamin Kaufmann and Torsten Schaub}, year = {2012}, title = {Conflict-driven answer set solving: From theory to practice}, journal = {Artif. Intell.}, volume = {187}, pages = {52--89}, doi = {10.1016/j.artint.2012.04.001}, ) @inproceedings(gebseradvanced2013, author = {Martin Gebser and Benjamin Kaufmann and Torsten Schaub}, year = {2013}, title = {Advanced Conflict-Driven Disjunctive Answer Set Solving}, editor = {Francesca Rossi}, booktitle = {{IJCAI} 2013, Proceedings of the 23rd International Joint Conference on Artificial Intelligence, Beijing, China, August 3-9, 2013}, publisher = {{IJCAI/AAAI}}, pages = {912--918}, url = {http://www.aaai.org/ocs/index.php/IJCAI/IJCAI13/paper/view/6835}, ) @inproceedings(heyninckapproximation2021, author = {Jesse Heyninck and Ofer Arieli}, year = {2021}, title = {Approximation Fixpoint Theory for Non-Deterministic Operators and Its Application in Disjunctive Logic Programming}, editor = {Meghyn Bienvenu and Gerhard Lakemeyer and Esra Erdem}, booktitle = {Proceedings of the 18th International Conference on Principles of Knowledge Representation and Reasoning, {KR} 2021, Online event, November 3-12, 2021}, pages = {334--344}, doi = {10.24963/kr.2021/32}, ) @article(Ji17, author = {Jianmin Ji and Fangfang Liu and Jia{-}Huai You}, year = {2017}, title = {Well-founded operators for normal hybrid {MKNF} knowledge bases}, journal = {Theory Pract. Log. Program.}, volume = {17}, number = {5-6}, pages = {889--905}, doi = {10.1017/S1471068417000291}, ) @inproceedings(kaminskiefficient2015, author = {Tobias Kaminski and Matthias Knorr and Jo{\~{a}}o Leite}, year = {2015}, title = {Efficient Paraconsistent Reasoning with Ontologies and Rules}, editor = {Qiang Yang and Michael J. Wooldridge}, booktitle = {Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, {IJCAI} 2015, Buenos Aires, Argentina, July 25-31, 2015}, publisher = {{AAAI} Press}, pages = {3098--3105}, url = {http://ijcai.org/Abstract/15/437}, ) @inproceedings(killenfixpoint2021, author = {Spencer Killen and Jia{-}Huai You}, year = {2021}, title = {Fixpoint Characterizations of Disjunctive Hybrid {MKNF} Knowledge Bases}, booktitle = {Proceedings of the International Conference on Logic Programming 2021 Workshops co-located with the 37th International Conference on Logic Programming {(ICLP} 2021), Porto, Portugal (virtual), September 20th-21st, 2021}, series = {{CEUR} Workshop Proceedings}, volume = {2970}, publisher = {CEUR-WS.org}, url = {http://ceur-ws.org/Vol-2970/aspocppaper3.pdf}, ) @inproceedings(killenunfounded, author = {Spencer Killen and Jia{-}Huai You}, year = {2021}, title = {Unfounded Sets for Disjunctive Hybrid {MKNF} Knowledge Bases}, editor = {Meghyn Bienvenu and Gerhard Lakemeyer and Esra Erdem}, booktitle = {Proceedings of the 18th International Conference on Principles of Knowledge Representation and Reasoning, {KR} 2021, Online event, November 3-12, 2021}, pages = {432--441}, doi = {10.24963/kr.2021/41}, ) @article(knorrlocal2011, author = {Matthias Knorr and Jos{\'{e}} J{\'{u}}lio Alferes and Pascal Hitzler}, year = {2011}, title = {Local closed world reasoning with description logics under the well-founded semantics}, journal = {Artif. Intell.}, volume = {175}, number = {9-10}, pages = {1528--1554}, doi = {10.1016/j.artint.2011.01.007}, ) @inproceedings(lifschitznonmonotonic1991, author = {Vladimir Lifschitz}, year = {1991}, title = {Nonmonotonic Databases and Epistemic Queries}, editor = {John Mylopoulos and Raymond Reiter}, booktitle = {Proceedings of the 12th International Joint Conference on Artificial Intelligence. Sydney, Australia, August 24-30, 1991}, publisher = {Morgan Kaufmann}, pages = {381--386}, url = {http://ijcai.org/Proceedings/91-1/Papers/059.pdf}, ) @article(liuthreevalued2017, author = {Fangfang Liu and Jia{-}Huai You}, year = {2017}, title = {Three-valued semantics for hybrid {MKNF} knowledge bases revisited}, journal = {Artif. Intell.}, volume = {252}, pages = {123--138}, doi = {10.1016/j.artint.2017.08.003}, ) @article(liuyou2021, author = {Fangfang Liu and Jia{-}Huai You}, year = {2022}, title = {Alternating Fixpoint Operator for Hybrid {MKNF} Knowledge Bases as an Approximator of {AFT}}, journal = {Theory Pract. Log. Program.}, volume = {22}, number = {2}, pages = {305--334}, doi = {10.1017/S1471068421000168}, ) @article(motikreconciling2010, author = {Boris Motik and Riccardo Rosati}, year = {2010}, title = {Reconciling description logics and rules}, journal = {J. {ACM}}, volume = {57}, number = {5}, pages = {30:1--30:62}, doi = {10.1145/1754399.1754403}, ) @article(przymusinskistable1991, author = {Teodor C. Przymusinski}, year = {1991}, title = {Stable Semantics for Disjunctive Programs}, journal = {New Gener. Comput.}, volume = {9}, number = {3/4}, pages = {401--424}, doi = {10.1007/BF03037171}, ) @article(tarskilatticetheoretical1955, author = {Alfred Tarski}, year = {1955}, title = {{A lattice-theoretical fixpoint theorem and its applications.}}, journal = {Pacific Journal of Mathematics}, volume = {5}, number = {2}, pages = {285 -- 309}, doi = {10.2140/pjm.1955.5.285}, )