{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T04:24:52Z","timestamp":1768451092697,"version":"3.49.0"},"reference-count":48,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T00:00:00Z","timestamp":1609804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Danish Council for Independent Research, Natural Sciences","award":["DFF-7014-00041"],"award-info":[{"award-number":["DFF-7014-00041"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2021,1,31]]},"abstract":"<jats:p>\n            Approximation fixpoint theory (AFT) is an algebraic study of fixpoints of lattice operators that unifies various knowledge representation formalisms. In AFT, stratification of operators has been studied, essentially resulting in a theory that specifies when certain types of fixpoints can be computed stratum per stratum. Recently, novel types of fixpoints related to\n            <jats:italic>groundedness<\/jats:italic>\n            have been introduced in AFT. In this article, we study how those fixpoints behave under stratified operators.\n          <\/jats:p>\n          <jats:p>\n            One recent application domain of AFT is the field of\n            <jats:italic>active integrity constraints<\/jats:italic>\n            (AICs). We apply our extended stratification theory to AICs and find that existing notions of stratification in AICs are covered by this general algebraic definition of stratification. As a result, we obtain stratification results for a large variety of semantics for AICs.\n          <\/jats:p>","DOI":"10.1145\/3430750","type":"journal-article","created":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T18:14:11Z","timestamp":1609870451000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Stratification in Approximation Fixpoint Theory and Its Application to Active Integrity Constraints"],"prefix":"10.1145","volume":"22","author":[{"given":"Bart","family":"Bogaerts","sequence":"first","affiliation":[{"name":"Vrije Universiteit Brussel (VUB), Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lu\u00eds","family":"Cruz-Filipe","sequence":"additional","affiliation":[{"name":"University of Southern Denmark, Odense, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2021,1,5]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the 2nd International Conference on Database Theory. 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Springer, 26--40."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068410000475"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.29007\/4n46"},{"key":"e_1_2_1_12_1","volume-title":"Logic and Data Bases","author":"Clark Keith L.","unstructured":"Keith L. Clark . 1978. Negation as failure . In Logic and Data Bases . Plenum Press , 293--322. Keith L. Clark. 1978. Negation as failure. In Logic and Data Bases. Plenum Press, 293--322."},{"key":"e_1_2_1_13_1","volume-title":"Proceedings of the 8th International Symposium on Foundations of Information and Knowledge Systems (FoIKS\u201914)","volume":"8367","author":"Cruz-Filipe Lu\u00eds","year":"2014","unstructured":"Lu\u00eds Cruz-Filipe . 2014 . Optimizing computation of repairs from active integrity constraints . In Proceedings of the 8th International Symposium on Foundations of Information and Knowledge Systems (FoIKS\u201914) . 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(Lecture Notes in Computer Science), Chitta Baral, Gerhard Brewka, and John S. Schlipf (Eds.), Vol. 4483. Springer, 84--96. DOI:https:\/\/doi.org\/10.1007\/978-3-540-72200-7_9"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/261124.261126"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0743-1066(85)80005-4"},{"key":"e_1_2_1_25_1","volume-title":"Proceedings of the 6th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, Eugenio Moggi and David Scott Warren (Eds.). ACM, 98--107","author":"Flesca Sergio","year":"2004","unstructured":"Sergio Flesca , Sergio Greco , and Ester Zumpano . 2004 . Active integrity constraints . In Proceedings of the 6th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, Eugenio Moggi and David Scott Warren (Eds.). ACM, 98--107 . DOI:https:\/\/doi.org\/10.1145\/1013963.1013977 10.1145\/1013963.1013977 Sergio Flesca, Sergio Greco, and Ester Zumpano. 2004. Active integrity constraints. In Proceedings of the 6th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, Eugenio Moggi and David Scott Warren (Eds.). ACM, 98--107. DOI:https:\/\/doi.org\/10.1145\/1013963.1013977"},{"key":"e_1_2_1_26_1","volume-title":"Proceedings of the International Conference on Logic Programming (ICLP\u201988) and Symposium on Logic Programming Conference (SLP\u201988)","author":"Gelfond Michael","year":"1988","unstructured":"Michael Gelfond and Vladimir Lifschitz . 1988 . The stable model semantics for logic programming . In Proceedings of the International Conference on Logic Programming (ICLP\u201988) and Symposium on Logic Programming Conference (SLP\u201988) , Robert A. Kowalski and Kenneth A. Bowen (Eds.). The MIT Press, 1070--1080. Retrieved from http:\/\/citeseer.ist.psu.edu\/viewdoc\/summary?doi&equals;10.1.1.24.6050. Michael Gelfond and Vladimir Lifschitz. 1988. The stable model semantics for logic programming. In Proceedings of the International Conference on Logic Programming (ICLP\u201988) and Symposium on Logic Programming Conference (SLP\u201988), Robert A. Kowalski and Kenneth A. Bowen (Eds.). The MIT Press, 1070--1080. Retrieved from http:\/\/citeseer.ist.psu.edu\/viewdoc\/summary?doi&equals;10.1.1.24.6050."},{"key":"e_1_2_1_27_1","volume-title":"Halpern and Yoram Moses","author":"Joseph","year":"1985","unstructured":"Joseph Y. Halpern and Yoram Moses . 1985 . Towards a theory of knowledge and ignorance: Preliminary report. In Logics and Models of Concurrent Systems. (NATO ASI Series), Krzysztof R. Apt (Ed.), Vol. 13 . Springer Berlin , 459--476. DOI:https:\/\/doi.org\/10.1007\/978-3-642-82453-1_16 10.1007\/978-3-642-82453-1_16 Joseph Y. Halpern and Yoram Moses. 1985. Towards a theory of knowledge and ignorance: Preliminary report. In Logics and Models of Concurrent Systems. (NATO ASI Series), Krzysztof R. Apt (Ed.), Vol. 13. Springer Berlin, 459--476. DOI:https:\/\/doi.org\/10.1007\/978-3-642-82453-1_16"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.2307\/2267778"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(88)90021-5"},{"key":"e_1_2_1_30_1","volume-title":"Proceedings of the 11th International Conference on Logic Programming, Pascal Van Hentenryck (Ed.). The MIT Press, 23--37","author":"Lifschitz Vladimir","year":"1994","unstructured":"Vladimir Lifschitz and Hudson Turner . 1994 . Splitting a logic program . In Proceedings of the 11th International Conference on Logic Programming, Pascal Van Hentenryck (Ed.). The MIT Press, 23--37 . Vladimir Lifschitz and Hudson Turner. 1994. Splitting a logic program. In Proceedings of the 11th International Conference on Logic Programming, Pascal Van Hentenryck (Ed.). The MIT Press, 23--37."},{"key":"e_1_2_1_31_1","volume-title":"Proceedings of the 29th Canadian Conference on Artificial Intelligence (Canadian AI\u201916)","volume":"9673","author":"Liu Fangfang","year":"2016","unstructured":"Fangfang Liu , Yi Bi , Md. Solimul Chowdhury , Jia-Huai You , and Zhiyong Feng . 2016 . Flexible approximators for approximating fixpoint theory . In Proceedings of the 29th Canadian Conference on Artificial Intelligence (Canadian AI\u201916) . (Lecture Notes in Computer Science), Richard Khoury and Christopher Drummond (Eds.) , Vol. 9673 . Springer, 224--236. DOI:https:\/\/doi.org\/10.1007\/978-3-319-34111-8_28 10.1007\/978-3-319-34111-8_28 Fangfang Liu, Yi Bi, Md. Solimul Chowdhury, Jia-Huai You, and Zhiyong Feng. 2016. Flexible approximators for approximating fixpoint theory. In Proceedings of the 29th Canadian Conference on Artificial Intelligence (Canadian AI\u201916). (Lecture Notes in Computer Science), Richard Khoury and Christopher Drummond (Eds.), Vol. 9673. Springer, 224--236. DOI:https:\/\/doi.org\/10.1007\/978-3-319-34111-8_28"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(97)00092-3"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/582410.582411"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(85)90042-6"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/311531.311623"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068406002973"},{"key":"e_1_2_1_37_1","doi-asserted-by":"crossref","unstructured":"Teodor C. Przymusinski. 1988. On the declarative semantics of deductive databases and logic programs. In Foundations of Deductive Databases and Logic Programming. Jack Minker (Ed.). Morgan Kaufmann 193--216.  Teodor C. Przymusinski. 1988. On the declarative semantics of deductive databases and logic programs. In Foundations of Deductive Databases and Logic Programming. Jack Minker (Ed.). Morgan Kaufmann 193--216.","DOI":"10.1016\/B978-0-934613-40-8.50009-9"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0743-1066(96)00091-X"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(80)90014-4"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2013.09.004"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2015.05.003"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01237920"},{"key":"e_1_2_1_43_1","first-page":"3","article-title":"Strong and uniform equivalence of nonmonotonic theories\u2014An algebraic approach","volume":"48","author":"Truszczy\u0144ski Miros\u0142aw","year":"2006","unstructured":"Miros\u0142aw Truszczy\u0144ski . 2006 . 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DOI:https:\/\/doi.org\/10.1145\/116825.116838 10.1145\/116825.116838 Allen Van Gelder, Kenneth A. Ross, and John S. Schlipf. 1991. The well-founded semantics for general logic programs. J. ACM 38, 3 (1991), 620--650. DOI:https:\/\/doi.org\/10.1145\/116825.116838","journal-title":"J. ACM"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1145\/1182613.1189735"},{"key":"e_1_2_1_47_1","unstructured":"Jennifer Widom and Stefano Ceri (Eds.). 1996. Active Database Systems: Triggers and Rules for Advanced Database Processing. Morgan Kaufmann.  Jennifer Widom and Stefano Ceri (Eds.). 1996. Active Database Systems: Triggers and Rules for Advanced Database Processing. Morgan Kaufmann."},{"key":"e_1_2_1_48_1","volume-title":"Updating Logical Databases","author":"Winslett Marianne","unstructured":"Marianne Winslett . 1990. Updating Logical Databases . (Cambridge Tracts in Theoretical Computer Science), Vol. 9 . Cambridge University Press . Marianne Winslett. 1990. 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