{"type":"ScholarlyArticle","title":"Semantics for Active Integrity Constraints Using Approximation Fixpoint Theory","authors":[{"name":"Bart Bogaerts","slug":"bart-bogaerts","given":"Bart","family":"Bogaerts","affiliation":"† KU Leuven , Department of Computer Science Celestijnenlaan 200A , Leuven , Belgium"},{"name":"Luís Cruz-Filipe","slug":"luis-cruz-filipe","given":"Luís","family":"Cruz-Filipe","affiliation":"‡ University of Southern Denmark , Department of Mathematics and Computer Science Campusvej 55 , Odense , Denmark"}],"abstract":"Active integrity constraints (AICs) constitute a formalism to associate with a database not just the constraints it should adhere to, but also how to fix the database in case one or more of these constraints are violated. The intuitions regarding which repairs are “good” given such a description are closely related to intuitions that live in various areas of non-monotonic reasoning.\r\nIn this paper, we apply approximation fixpoint theory, an algebraic framework that unifies semantics of non-monotonic logics, to the field of AICs.\r\nThis results in a new family of semantics for AICs, of which we study semantics and relationships to existing semantics. We argue that the AFT-well-founded semantics has some desirable properties.","doi":"10.24963/ijcai.2017/120","url":"https://ijcai.org/proceedings/2017/120","pdf":"https://ijcai.org/proceedings/2017/0120.pdf","markdown":"https://ijcai.org/proceedings/2017/120.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/120","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Knowledge Representation, Reasoning, and Logic","track":"Main track","number":120,"pages":{"first":866,"last":872},"keywords":["Multidisciplinary Topics and Applications: Database Systems","Knowledge Representation, Reasoning, and Logic: Knowledge Representation Languages","Knowledge Representation, Reasoning, and Logic: Non-monotonic Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Abiteboul, 1988] Serge Abiteboul. Updates, a new frontier. In Marc Gyssens, Jan Paredaens, and Dirk van Gucht, editors, ICDT, volume 326 of LNCS, pages 1-18. Springer, 1988.","title":"Updates, a new frontier","authors":"Serge Abiteboul","year":"1988","venue":"ICDT","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bi et al., 2014] Yi Bi, Jia-Huai You, and Zhiyong Feng. A gen- eralization of approximation fixpoint theory and application. In Proceedings of RR, pages 45-59, 2014.","title":"A generalization of approximation fixpoint theory and application","authors":"Yi Bi, Jia-Huai You, Zhiyong Feng","year":"2014","venue":"Proceedings of RR","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bogaerts et al., 2015a] Bart Bogaerts, Joost Vennekens, and Marc Denecker. Grounded fixpoints and their applications in knowl- edge representation. AIJ, 224:51-71, 2015.","title":"Grounded fixpoints and their applications in knowledge representation","authors":"Bogaerts","year":"2015","venue":"AIJ","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bogaerts et al., 2015b] Bart Bogaerts, Joost Vennekens, and Marc Denecker. Partial grounded fixpoints. In Proceedings of IJCAI, pages 2784-2790, 2015.","title":"Partial grounded fixpoints","authors":"Bogaerts","year":"2015","venue":"Proceedings of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/394"},{"position":5,"raw":"[Bogaerts et al., 2016] Bart Bogaerts, Joost Vennekens, and Marc Denecker. On well-founded set-inductions and locally mono- tone operators. ACM Trans. Comput. Logic, 17(4):27:1-27:32, September 2016.","title":"On well-founded set-inductions and locally monotone operators","authors":"Bart Bogaerts, Joost Vennekens, Marc Denecker","year":"2016","venue":"ACM Trans. Comput. Logic","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bogaerts et al., 2017] Bart Bogaerts, Joost Vennekens, and Marc Denecker. Safe inductions: An algebraic study. In Proceedings of IJCAI, 2017. (to appear).","title":"Safe inductions: An algebraic study","authors":"Bart Bogaerts, Joost Vennekens, Marc Denecker","year":"2017","venue":"Proceedings of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2017/119"},{"position":7,"raw":"[Brewka and Woltran, 2010] Gerhard Brewka and Stefan Woltran. Abstract dialectical frameworks. In Proceedings of KR, pages 102-111, 2010.","title":"Abstract dialectical frameworks","authors":"Gerhard Brewka, Stefan Woltran","year":"2010","venue":"Proceedings of KR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Caroprese and Truszczyński, 2011] Luciano Caroprese and Mirosław Truszczyński. Active integrity constraints and revision programming. TPLP, 11(6):905-952, 2011.","title":"Active integrity constraints and revision programming","authors":"Luciano Caroprese, Mirosław Truszczyński","year":"2011","venue":"TPLP","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Caroprese et al., 2006] Luciano Caroprese, Sergio Greco, Cristina Sirangelo, and Ester Zumpano. Declarative semantics of produc- tion rules for integrity maintenance. In Proceedings of ICLP, pages 26-40, 2006.","title":"Declarative semantics of production rules for integrity maintenance","authors":"Luciano Caroprese, Sergio Greco, Cristina Sirangelo, Ester Zumpano","year":"2006","venue":"Proceedings of ICLP","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Cruz-Filipe et al., 2013] Luís Cruz-Filipe, Grac ¸a Gaspar, Patrícia Engrácia, and Isabel Nunes. Computing repairs from active in- tegrity constraints. In TASE 2013, pages 183-190. IEEE Com- puter Society, 2013.","title":"Computing repairs from active integrity constraints","authors":"Luís Cruz-Filipe, Patrícia Grac ¸a Gaspar, Isabel Engrácia, Nunes","year":"2013","venue":"TASE 2013","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Cruz-Filipe et al., 2015] Luís Cruz-Filipe, Michael Franz, Ar- tavazd Hakhverdyan, Marta Ludovico, Isabel Nunes, and Peter Schneider-Kamp. repAIrC: A tool for ensuring data consistency by means of active integrity constraints. In Proceedings of KMIS, volume 3, pages 17-26, 2015.","title":"repAIrC: A tool for ensuring data consistency by means of active integrity constraints","authors":"Luís Cruz-Filipe, Michael Franz, Artavazd Hakhverdyan, Marta Ludovico, Isabel Nunes, Peter Schneider-Kamp","year":"2015","venue":"Proceedings of KMIS","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"Luís Cruz-Filipe. Optimizing computation of repairs from active integrity constraints. In Proceedings of FoIKS, pages 361-380, 2014.","title":"Optimizing computation of repairs from active integrity constraints","authors":"Luís Cruz-Filipe","year":"2014","venue":"Proceedings of FoIKS","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"Luís Cruz-Filipe. Grounded fixpoints and ac- tive integrity constraints. In Technical communications of ICLP, pages 11.1-11.14, 2016.","title":"Grounded fixpoints and active integrity constraints","authors":"Luís Cruz-Filipe","year":"2016","venue":"Technical communications of ICLP","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Denecker and Vennekens, 2007] Marc Denecker and Joost Ven- nekens. Well-founded semantics and the algebraic theory of non-monotone inductive definitions. In Proceedings of LPNMR, pages 84-96, 2007.","title":"Well-founded semantics and the algebraic theory of non-monotone inductive definitions","authors":"Marc Denecker, Joost Vennekens","year":"2007","venue":"Proceedings of LPNMR","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Denecker et al., 2000] Marc Denecker, Victor Marek, and Mirosław Truszczyński. Approximations, stable operators, well- founded fixpoints and applications in nonmonotonic reasoning. In Logic-Based Artificial Intelligence, Springer, volume 597, pages 127-144, 2000.","title":"Approximations, stable operators, wellfounded fixpoints and applications in nonmonotonic reasoning","authors":"Marc Denecker, Victor Marek, Mirosław Truszczyński","year":"2000","venue":"Logic-Based Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Denecker et al., 2003] Marc Denecker, Victor Marek, and Mirosław Truszczyński. Uniform semantic treatment of default and autoepistemic logics. AIJ, 143(1):79-122, 2003.","title":"Uniform semantic treatment of default and autoepistemic logics","authors":"Marc Denecker, Victor Marek, Mirosław Truszczyński","year":"2003","venue":"AIJ","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Denecker et al., 2004] Marc Denecker, Victor Marek, and Mirosław Truszczyński. Ultimate approximation and its ap- plication in nonmonotonic knowledge representation systems. Information and Computation, 192(1):84-121, July 2004.","title":"Ultimate approximation and its application in nonmonotonic knowledge representation systems","authors":"Denecker","year":"2004","venue":"Information and Computation","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Dung, 1995] Phan Minh Dung. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic pro- gramming and n-person games. AI, 77(2):321 -357, 1995.","title":"On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games","authors":"Phan Minh, Dung","year":"1995","venue":"AI","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Eiter and Gottlob, 1992] Thomas Eiter and Georg Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. AIJ, 57(2-3):227-270, 1992.","title":"On the complexity of propositional knowledge base revision, updates, and counterfactuals","authors":"Thomas Eiter, Georg Gottlob","year":"1992","venue":"AIJ","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Flesca et al., 2004] Sergio Flesca, Sergio Greco, and Ester Zumpano. Active integrity constraints. In Proceedings of SIG- PLAN, pages 98-107, 2004.","title":"Active integrity constraints","authors":"Sergio Flesca, Sergio Greco, Ester Zumpano","year":"2004","venue":"Proceedings of SIG-PLAN","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Kleene, 1938] Stephen Cole Kleene. On notation for ordinal num- bers. The Journal of Symbolic Logic, 3(4):150-155, 1938.","title":"On notation for ordinal numbers","authors":"Stephen Cole, Kleene","year":"1938","venue":"The Journal of Symbolic Logic","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Marek and Truszczynski, 1998] V. Wiktor Marek and Miroslaw Truszczynski. Revision programming. Theor. Comput. Sci., 190(2):241-277, 1998.","title":"Revision programming","authors":"V Wiktor Marek, Miroslaw Truszczynski","year":"1998","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Moore, 1985] Robert C. Moore. Semantical considerations on nonmonotonic logic. AIJ, 25(1):75-94, 1985.","title":"Semantical considerations on nonmonotonic logic","authors":"Robert C Moore","year":"1985","venue":"AIJ","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Przymusinski and Turner, 1997] Teodor C. Przymusinski and Hudson Turner. Update by means of inference rules. Journal of Logic Programming, 30(2):125-143, 1997.","title":"Update by means of inference rules","authors":"Teodor C Przymusinski, Hudson Turner","year":"1997","venue":"Journal of Logic Programming","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Reiter, 1980] Raymond Reiter. A logic for default reasoning. AIJ, 13(1-2):81-132, 1980.","title":"A logic for default reasoning","authors":"Raymond Reiter","year":"1980","venue":"AIJ","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Strass, 2013] Hannes Strass. Approximating operators and seman- tics for abstract dialectical frameworks. AIJ, 205:39-70, 2013.","title":"Approximating operators and semantics for abstract dialectical frameworks","authors":"Hannes Strass, Strass","year":"2013","venue":"AIJ","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Teniente and Olivé, 1995] Ernest Teniente and Antoni Olivé. Up- dating knowledge bases while maintaining their consistency. VLDB Journal, 4(2):193-241, 1995.","title":"Updating knowledge bases while maintaining their consistency","authors":"Olivé Teniente, Ernest Teniente, Antoni Olivé","year":"1995","venue":"VLDB Journal","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[van Emden and Kowalski, 1976] Maarten H. van Emden and Robert A. Kowalski. The semantics of predicate logic as a pro- gramming language. J. ACM, 23(4):733-742, 1976.","title":"The semantics of predicate logic as a programming language","authors":"Van Emden, H Kowalski ; ] Maarten, Robert A Van Emden, Kowalski","year":"1976","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Van Gelder et al., 1991] Allen Van Gelder, Kenneth A. Ross, and John S. Schlipf. The well-founded semantics for general logic programs. J. ACM, 38(3):620-650, 1991.","title":"The well-founded semantics for general logic programs","authors":"Allen Van Gelder, Kenneth A Ross, John S Schlipf","year":"1991","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Vennekens et al., 2006] Joost Vennekens, David Gilis, and Marc Denecker. Splitting an operator: Algebraic modularity results for logics with fixpoint semantics. ACM Trans. Comput. Log., 7(4):765-797, 2006.","title":"Splitting an operator: Algebraic modularity results for logics with fixpoint semantics","authors":"Vennekens","year":"2006","venue":"ACM Trans. Comput. Log","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Vennekens et al., 2007a] Joost Vennekens, Maarten Mariën, Johan Wittocx, and Marc Denecker. Predicate introduction for logics with a fixpoint semantics. Part I: Logic programming. Funda- menta Informaticae, 79(1-2):187-208, September 2007.","title":"Predicate introduction for logics with a fixpoint semantics. Part I: Logic programming","authors":"Vennekens","year":"2007","venue":"Fundamenta Informaticae","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Vennekens et al., 2007b] Joost Vennekens, Maarten Mariën, Johan Wittocx, and Marc Denecker. Predicate introduction for logics with a fixpoint semantics. Part II: Autoepistemic logic. Funda- menta Informaticae, 79(1-2):209-227, September 2007.","title":"Predicate introduction for logics with a fixpoint semantics. Part II: Autoepistemic logic","authors":"Vennekens","year":"2007","venue":"Fundamenta Informaticae","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Widom and Ceri, 1996] Jennifer Widom and Stefano Ceri, editors. Active Database Systems: Triggers and Rules For Advanced Database Processing.","title":"Active Database Systems: Triggers and Rules For Advanced Database Processing","authors":"Ceri Widom","year":"1996","venue":null,"doi":null,"url":null,"internal_url":null},{"position":34,"raw":"Morgan Kaufmann, 1996.","title":null,"authors":"Morgan Kaufmann","year":"1996","venue":null,"doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Winslett, 1990] Marianne Winslett. Updating Logical Databases. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1990.","title":"Updating Logical Databases","authors":"Marianne Winslett","year":"1990","venue":"Cambridge Tracts in Theoretical Computer Science","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}