{"type":"ScholarlyArticle","title":"Three-Valued Semantics for Hybrid MKNF Knowledge Bases Revisited (Extended Abstract)","authors":[{"name":"Fangfang Liu","slug":"fangfang-liu","given":"Fangfang","family":"Liu","affiliation":"Shanghai University , Shanghai , China"},{"name":"Jia-Huai You","slug":"jia-huai-you","given":"Jia-Huai","family":"You","affiliation":"University of Alberta , Edmonton , Canada"}],"abstract":"Knorr et al. (2011) formulated a three-valued formalism for the logic of Minimal Knowledge and Negation as Failure (MKNF) and proposed a well-founded semantics for hybrid MKNF knowledge bases (KBs).\r\nThe main results state that if a hybrid MKNF KB has a three-valued MKNF model, its well-founded MKNF model exists, which is unique and can be computed by an alternating fixpoint construction.  In this paper, we show that these claims are erroneous.  We propose a classification of hybrid MKNF KBs into a hierarchy and show that its innermost subclass is what works for the well-founded semantics of Knorr et al. Furthermore, we provide a uniform characterization of well-founded, two-valued, and all three-valued MKNF models, in terms of stable partitions and the alternating fixpoint construction, which leads to updated complexity results as well as proof-theoretic tools for reasoning under these semantics.","doi":"10.24963/ijcai.2018/798","url":"https://ijcai.org/proceedings/2018/798","pdf":"https://ijcai.org/proceedings/2018/0798.pdf","markdown":"https://ijcai.org/proceedings/2018/798.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/798","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Journal track","track":"Journal track","number":798,"pages":{"first":5627,"last":5631},"keywords":["Knowledge Representation and Reasoning: Description Logics and Ontologies","Knowledge Representation and Reasoning: Non-monotonic Reasoning","Knowledge Representation and Reasoning: Logics for Knowledge Representation","Knowledge Representation and Reasoning: Knowledge Representation Languages"],"videos":[],"references":[{"position":1,"raw":"[Bruijn et al., 2007] J. Bruijn, T. Eiter, A. Polleres, and H. Tompits. Embedding non-ground logic programs into autoepistemic logic for knowledge-base combination. In Proceedings of International Joint Conference On Artifi- cial Intelligence, IJCAI 2007, pages 304-309, 2007.","title":"Embedding non-ground logic programs into autoepistemic logic for knowledge-base combination","authors":"J Bruijn, T Eiter, A Polleres, H Tompits","year":"2007","venue":"Proceedings of International Joint Conference On Artificial Intelligence, IJCAI 2007","doi":null,"url":null,"internal_url":"/proceedings/2007/47"},{"position":2,"raw":"[Denecker et al., 2004] Marc Denecker, Victor W. Marek, and Miroslaw Truszczynski. Ultimate approximation and its application in nonmonotonic knowledge representation systems. Information and Computation, 192(1):84-121, 2004.","title":"Ultimate approximation and its application in nonmonotonic knowledge representation systems","authors":"Marc Denecker, Victor W Marek, Miroslaw Truszczynski","year":"2004","venue":"Information and Computation","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Eiter et al., 2005] Thomas Eiter, Giovambattista Ianni, Ro- man Schindlauer, and Hans Tompits. A uniform integra- tion of higher-order reasoning and external evaluations in answer-set programming. In Proc. Nineteenth Interna- tional Joint Conference on Artificial Intelligence, IJCAI 2005, pages 90-96, Edinburdh, Scotland, 2005.","title":"A uniform integration of higher-order reasoning and external evaluations in answer-set programming","authors":"Thomas Eiter, Giovambattista Ianni, Roman Schindlauer, Hans Tompits","year":"2005","venue":"Proc. Nineteenth International Joint Conference on Artificial Intelligence, IJCAI 2005","doi":null,"url":null,"internal_url":"/proceedings/2005/169"},{"position":4,"raw":"[Morgan Kaufmann. Kaminski et al., 2015] Tobias Kaminski, Matthias Knorr, and João Leite. Efficient paraconsistent reasoning with on- tologies and rules. In Proc. Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, pages 3098-3105, Buenos Aires, Argentina, 2015.","title":"Efficient paraconsistent reasoning with ontologies and rules","authors":"Morgan Kaufmann, Kaminski","year":"2015","venue":"Proc. Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015","doi":null,"url":null,"internal_url":"/proceedings/2015/437"},{"position":5,"raw":"[Mor- gan Kaufmann. Knorr et al., 2011] Matthias Knorr, José Júlio Alferes, and Pascal Hitzler. Local closed world reasoning with descrip- tion logics under the well-founded semantics. Artificial Intelligence, 175(9-10):1528-1554, 2011.","title":"Local closed world reasoning with description logics under the well-founded semantics","authors":"Morgan Kaufmann, Knorr","year":"2011","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Lifschitz, 1991] Vladimir Lifschitz. Nonmonotonic databases and epistemic queries. In Proc. 12th Interna- tional Joint Conference on Artificial Intelligence, IJCAI 1991, pages 381-386, Sydney, Australia, 1991.","title":"Nonmonotonic databases and epistemic queries","authors":"Vladimir Lifschitz","year":"1991","venue":"Proc. 12th International Joint Conference on Artificial Intelligence, IJCAI 1991","doi":null,"url":null,"internal_url":"/proceedings/1991/57"},{"position":7,"raw":"[Motik and Rosati, 2007] Boris Motik and Riccardo Rosati. A faithful integration of description logics with logic pro- gramming. In Proc. Nineteenth International Joint Con- ference on Artificial Intelligence, IJCAI 2007, pages 477- 482, Hyderabad, India, 2007.","title":"A faithful integration of description logics with logic programming","authors":"Rosati Motik, Boris Motik, Riccardo Rosati","year":"2007","venue":"Proc. Nineteenth International Joint Conference on Artificial Intelligence, IJCAI 2007","doi":null,"url":null,"internal_url":"/proceedings/2007/75"},{"position":8,"raw":"Morgan Kaufmann.","title":null,"authors":"Morgan Kaufmann","year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Motik and Rosati, 2010] Boris Motik and Riccardo Rosati. Reconciling description logics and rules. Journal of the ACM, 57(5):1-62, 2010.","title":"Reconciling description logics and rules","authors":"Rosati Motik, Boris Motik, Riccardo Rosati","year":"2010","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Przymusinski, 1990] Teodor C. Przymusinski. The well- founded semantics coincides with the three-valued sta- ble semantics. Fundamenta Informaticae, 13(4):445-463, 1990.","title":"The wellfounded semantics coincides with the three-valued stable semantics","authors":"Teodor C Przymusinski","year":"1990","venue":"Fundamenta Informaticae","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Rosati, 2006] Riccardo Rosati. DL+log: Tight integration of description logics and disjunctive datalog. In Proc. 10th International Conference on Principles of Knowledge Representation and Reasoning, KR 2006, pages 68-78, Lake District, UK, 2006. AAAI Press.","title":"DL+log: Tight integration of description logics and disjunctive datalog","authors":"Riccardo Rosati","year":"2006","venue":"Proc. 10th International Conference on Principles of Knowledge Representation and Reasoning","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Vennekens et al., 2010] Joost Vennekens, Marc Denecker, and Maurice Bruynooghe. FO(ID) as an extension of DL with rules. Annals of Mathematics and Artificial Intelli- gence, 58(1-2):85-115, 2010.","title":"FO(ID) as an extension of DL with rules","authors":"Joost Vennekens, Marc Denecker, Maurice Bruynooghe","year":"2010","venue":"Annals of Mathematics and Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Yang et al., 2011] Qian Yang, Jia-Huai You, and Zhiyong Feng. Integrating rules and description logics by circum- scription. In Proc. Twenty-Fifth Conference on Artificial Intelligence, AAAI 2011, San Francisco, California, 2011. AAAI Press.","title":"Integrating rules and description logics by circumscription","authors":"Qian Yang, Jia-Huai You, Zhiyong Feng","year":"2011","venue":"Proc. Twenty-Fifth Conference on Artificial Intelligence, AAAI 2011","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[You and Yuan, 1994] Jia-Huai You and Li-Yan Yuan. A three-valued semantics for deductive databases and logic programs. Journal of Computer System and Sciences, 49(2):334-361, 1994.","title":"A three-valued semantics for deductive databases and logic programs","authors":"Jia-Huai You, Li-Yan Yuan","year":"1994","venue":"Journal of Computer System and Sciences","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}