{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T15:08:58Z","timestamp":1760800138313,"version":"3.41.0"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2018,7,2]],"date-time":"2018-07-02T00:00:00Z","timestamp":1530489600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001509","name":"Royal Society of New Zealand","doi-asserted-by":"publisher","award":["Marsden Fast Start Grant","Marsden Research Grant"],"award-info":[{"award-number":["Marsden Fast Start Grant","Marsden Research Grant"]}],"id":[{"id":"10.13039\/501100001509","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["The VLDB Journal"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s00778-018-0511-z","type":"journal-article","created":{"date-parts":[[2018,7,2]],"date-time":"2018-07-02T06:48:41Z","timestamp":1530514121000},"page":"771-795","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Probabilistic Cardinality Constraints"],"prefix":"10.1007","volume":"27","author":[{"given":"Tania","family":"Roblot","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miika","family":"Hannula","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1816-2863","authenticated-orcid":false,"given":"Sebastian","family":"Link","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,7,2]]},"reference":[{"key":"511_CR1","volume-title":"Foundations of Databases","author":"S Abiteboul","year":"1995","unstructured":"Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Boston (1995)"},{"key":"511_CR2","doi-asserted-by":"crossref","unstructured":"Armstrong, W.W.: Dependency structures of data base relationships. In: IFIP Congress, pp. 580\u2013583 (1974)","DOI":"10.1515\/9783110840308-026"},{"key":"511_CR3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804090","volume-title":"Computational Complexity: A Modern Approach","author":"S Arora","year":"2009","unstructured":"Arora, S., Barak, B.: Computational Complexity: A Modern Approach, 1st edn. Cambridge University Press, New York (2009)","edition":"1"},{"issue":"1\u20132","key":"511_CR4","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S0004-3702(96)00010-0","volume":"88","author":"F Baader","year":"1996","unstructured":"Baader, F., Buchheit, M., Hollunder, B.: Cardinality restrictions on concepts. Artif. Intell. 88(1\u20132), 195\u2013213 (1996)","journal-title":"Artif. Intell."},{"key":"511_CR5","volume-title":"Structural Complexity I","author":"JL Balcazar","year":"2012","unstructured":"Balcazar, J.L., Diaz, J., Gabarro, J.: Structural Complexity I. Springer, Berlin (2012)"},{"issue":"1","key":"511_CR6","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1145\/2422.322414","volume":"31","author":"C Beeri","year":"1984","unstructured":"Beeri, C., Dowd, M., Fagin, R., Statman, R.: On the structure of Armstrong relations for functional dependencies. J. ACM 31(1), 30\u201346 (1984)","journal-title":"J. ACM"},{"issue":"1\u20132","key":"511_CR7","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.artint.2005.05.003","volume":"168","author":"D Berardi","year":"2005","unstructured":"Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artif. Intell. 168(1\u20132), 70\u2013118 (2005)","journal-title":"Artif. Intell."},{"key":"511_CR8","doi-asserted-by":"crossref","unstructured":"Biskup, J., Menzel, R., Polle, T., Sagiv, Y.: Decomposition of relationships through pivoting. In: ER, pp. 28\u201341 (1996)","DOI":"10.1007\/BFb0019913"},{"key":"511_CR9","doi-asserted-by":"crossref","unstructured":"Brown, P., Ganesan, J., K\u00f6hler, H., Link, S.: Keys with probabilistic intervals. In: ER, pp. 164\u2013179 (2016)","DOI":"10.1007\/978-3-319-46397-1_13"},{"key":"511_CR10","doi-asserted-by":"crossref","unstructured":"Brown, P., Link, S.: Probabilistic keys for data quality management. In: CAiSE, pp. 118\u2013132 (2015)","DOI":"10.1007\/978-3-319-19069-3_8"},{"issue":"3","key":"511_CR11","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1109\/TKDE.2016.2633342","volume":"29","author":"P Brown","year":"2017","unstructured":"Brown, P., Link, S.: Probabilistic keys. IEEE Trans. Knowl. Data Eng. 29(3), 670\u2013682 (2017)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"issue":"12","key":"511_CR12","doi-asserted-by":"publisher","first-page":"1721","DOI":"10.1109\/TKDE.2006.190","volume":"18","author":"N Bruno","year":"2006","unstructured":"Bruno, N., Chaudhuri, S., Thomas, D.: Generating queries with cardinality constraints for DBMS testing. IEEE Trans. Knowl. Data Eng. 18(12), 1721\u20131725 (2006)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"511_CR13","doi-asserted-by":"crossref","unstructured":"Calvanese, D., Lenzerini, M.: On the interaction between ISA and cardinality constraints. In: ICDE, pp. 204\u2013213 (1994)","DOI":"10.1109\/ICDE.1994.283032"},{"issue":"1","key":"511_CR14","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/0022-0000(84)90075-8","volume":"28","author":"MA Casanova","year":"1984","unstructured":"Casanova, M.A., Fagin, R., Papadimitriou, C.H.: Inclusion dependencies and their interaction with functional dependencies. J. Comput. Syst. Sci. 28(1), 29\u201359 (1984)","journal-title":"J. Comput. Syst. Sci."},{"key":"511_CR15","doi-asserted-by":"crossref","unstructured":"Chaudhuri, S.: Query optimizers: time to rethink the contract? In: SIGMOD, pp. 961\u2013968 (2009)","DOI":"10.1145\/1559845.1559955"},{"issue":"1","key":"511_CR16","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1145\/320434.320440","volume":"1","author":"PP Chen","year":"1976","unstructured":"Chen, P.P.: The Entity-Relationship model\u2014toward a unified view of data. ACM Trans. Database Syst. 1(1), 9\u201336 (1976)","journal-title":"ACM Trans. Database Syst."},{"issue":"14","key":"511_CR17","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1016\/j.ipl.2009.03.021","volume":"109","author":"W Chen","year":"2009","unstructured":"Chen, W., Fan, W., Ma, S.: Incorporating cardinality constraints and synonym rules into conditional functional dependencies. Inf. Process. Lett. 109(14), 783\u2013789 (2009)","journal-title":"Inf. Process. Lett."},{"key":"511_CR18","doi-asserted-by":"crossref","unstructured":"Cormode, G., Srivastava, D., Shen, E., Yu, T.: Aggregate query answering on possibilistic data with cardinality constraints. In: ICDE, pp. 258\u2013269 (2012)","DOI":"10.1109\/ICDE.2012.15"},{"issue":"4","key":"511_CR19","doi-asserted-by":"publisher","first-page":"952","DOI":"10.1145\/322344.322347","volume":"29","author":"R Fagin","year":"1982","unstructured":"Fagin, R.: Horn clauses and database dependencies. J. ACM 29(4), 952\u2013985 (1982)","journal-title":"J. ACM"},{"issue":"4","key":"511_CR20","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1016\/j.jcss.2006.10.013","volume":"73","author":"A Fuxman","year":"2007","unstructured":"Fuxman, A., Miller, R.J.: First-order query rewriting for inconsistent databases. J. Comput. Syst. Sci. 73(4), 610\u2013635 (2007)","journal-title":"J. Comput. Syst. Sci."},{"key":"511_CR21","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.datak.2015.06.002","volume":"99","author":"N Hall","year":"2015","unstructured":"Hall, N., K\u00f6hler, H., Link, S., Prade, H., Zhou, X.: Cardinality constraints on qualitatively uncertain data. Data Knowl. Eng. 99, 126\u2013150 (2015)","journal-title":"Data Knowl. Eng."},{"key":"511_CR22","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/978-3-540-49524-6_12","volume-title":"Conceptual Modeling \u2013 ER \u201998","author":"Sven Hartmann","year":"1998","unstructured":"Hartmann, S.: On the consistency of Int-cardinality constraints. In: ER, pp. 150\u2013163 (1998)"},{"issue":"2\u20134","key":"511_CR23","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1023\/A:1013133428451","volume":"33","author":"S Hartmann","year":"2001","unstructured":"Hartmann, S.: On the implication problem for cardinality constraints and functional dependencies. Ann. Math. Artif. Intell. 33(2\u20134), 253\u2013307 (2001)","journal-title":"Ann. Math. Artif. Intell."},{"key":"511_CR24","unstructured":"Hartmann, S.: Reasoning about participation constraints and chen\u2019s constraints. In: ADC, pp. 105\u2013113 (2003)"},{"issue":"1","key":"511_CR25","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s00778-011-0239-5","volume":"21","author":"S Hartmann","year":"2012","unstructured":"Hartmann, S., Kirchberg, M., Link, S.: Design by example for SQL table definitions with functional dependencies. VLDB J. 21(1), 121\u2013144 (2012)","journal-title":"VLDB J."},{"issue":"2","key":"511_CR26","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1145\/1538909.1538912","volume":"34","author":"S Hartmann","year":"2009","unstructured":"Hartmann, S., Link, S.: Efficient reasoning about a robust XML key fragment. ACM Trans. Database Syst. 34(2), 10 (2009)","journal-title":"ACM Trans. Database Syst."},{"issue":"5","key":"511_CR27","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1016\/j.ic.2008.09.004","volume":"208","author":"S Hartmann","year":"2010","unstructured":"Hartmann, S., Link, S.: Numerical constraints on XML data. Inf. Comput. 208(5), 521\u2013544 (2010)","journal-title":"Inf. Comput."},{"key":"511_CR28","doi-asserted-by":"crossref","unstructured":"Ilyas, I.F., Markl, V., Haas, P.J., Brown, P., Aboulnaga, A.: CORDS: automatic discovery of correlations and soft functional dependencies. In: SIGMOD, pp. 647\u2013658 (2004)","DOI":"10.1145\/1007568.1007641"},{"issue":"1","key":"511_CR29","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/0169-023X(95)00036-R","volume":"19","author":"TH Jones","year":"1996","unstructured":"Jones, T.H., Song, I.-Y.: Analysis of binary\/ternary cardinality combinations in Entity-Relationship modeling. Data Knowl. Eng. 19(1), 39\u201364 (1996)","journal-title":"Data Knowl. Eng."},{"key":"511_CR30","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.jcss.2016.11.004","volume":"85","author":"H K\u00f6hler","year":"2017","unstructured":"K\u00f6hler, H., Link, S.: Inclusion dependencies and their interaction with functional dependencies in SQL. J. Comput. Syst. Sci. 85, 104\u2013131 (2017)","journal-title":"J. Comput. Syst. Sci."},{"issue":"3","key":"511_CR31","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1016\/j.is.2009.11.002","volume":"35","author":"W-D Langeveldt","year":"2010","unstructured":"Langeveldt, W.-D., Link, S.: Empirical evidence for the usefulness of Armstrong relations in the acquisition of meaningful FDs. Inf. Syst. 35(3), 352\u2013374 (2010)","journal-title":"Inf. Syst."},{"key":"511_CR32","unstructured":"Lenzerini, M., Nobili, P.: On the satisfiability of dependency constraints in entity-relationship schemata. In: VLDB, pp. 147\u2013154 (1987)"},{"key":"511_CR33","doi-asserted-by":"crossref","unstructured":"Letchner, J., R\u00e9, C., Balazinska, M., Philipose, M.: Access methods for Markovian streams. In: ICDE, pp. 246\u2013257 (2009)","DOI":"10.1109\/ICDE.2009.21"},{"issue":"3","key":"511_CR34","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/0169-023X(93)90024-J","volume":"11","author":"SW Liddle","year":"1993","unstructured":"Liddle, S.W., Embley, D.W., Woodfield, S.N.: Cardinality constraints in semantic data models. Data Knowl. Eng. 11(3), 235\u2013270 (1993)","journal-title":"Data Knowl. Eng."},{"issue":"2","key":"511_CR35","first-page":"251","volume":"24","author":"J Liu","year":"2012","unstructured":"Liu, J., Li, J., Liu, C., Chen, Y.: Discover dependencies from data\u2014a review. IEEE TKDE 24(2), 251\u2013264 (2012)","journal-title":"IEEE TKDE"},{"issue":"2","key":"511_CR36","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/0022-0000(86)90015-2","volume":"33","author":"H Mannila","year":"1986","unstructured":"Mannila, H., R\u00e4ih\u00e4, K.-J.: Design by example: an application of armstrong relations. J. Comput. Syst. Sci. 33(2), 126\u2013141 (1986)","journal-title":"J. Comput. Syst. Sci."},{"issue":"3","key":"511_CR37","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1016\/j.is.2005.12.007","volume":"32","author":"FD Marchi","year":"2007","unstructured":"Marchi, F.D., Petit, J.: Semantic sampling of existing databases through informative Armstrong databases. Inf. Syst. 32(3), 446\u2013457 (2007)","journal-title":"Inf. Syst."},{"key":"511_CR38","volume-title":"Conceptual modeling of information systems","author":"A Oliv\u00e9","year":"2007","unstructured":"Oliv\u00e9, A.: Conceptual modeling of information systems. Springer, Berlin (2007)"},{"issue":"10","key":"511_CR39","first-page":"1154","volume":"10","author":"L Orr","year":"2017","unstructured":"Orr, L., Suciu, D., Balazinska, M.: Probabilistic database summarization for interactive data exploration. PVLDB 10(10), 1154\u20131165 (2017)","journal-title":"PVLDB"},{"key":"511_CR40","doi-asserted-by":"crossref","unstructured":"Roblot, T., Link, S.: Probabilistic cardinality constraints. In: ER, pp. 214\u2013228 (2015)","DOI":"10.1007\/978-3-319-25264-3_16"},{"key":"511_CR41","doi-asserted-by":"crossref","unstructured":"Roblot, T.K., Link, S.: Possibilistic cardinality constraints and functional dependencies. In ER, pp. 133\u2013148 (2016)","DOI":"10.1007\/978-3-319-46397-1_11"},{"key":"511_CR42","doi-asserted-by":"crossref","unstructured":"Roblot, T.K., Link, S.: URD: A data summarization tool for the acquisition of meaningful cardinality constraints with probabilistic intervals. In: ICDE, pp. 1379\u20131380 (2017)","DOI":"10.1109\/ICDE.2017.186"},{"key":"511_CR43","unstructured":"Shen, W., Li, X., Doan, A.: Constraint-based entity matching. In: AAAI, pp. 862\u2013867 (2005)"},{"issue":"2\/3","key":"511_CR44","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/S0306-4379(97)00009-4","volume":"22","author":"K Siau","year":"1997","unstructured":"Siau, K., Wand, Y., Benbasat, I.: The relative importance of structural constraints and surface semantics in information modeling. Inf. Syst. 22(2\/3), 155\u2013170 (1997)","journal-title":"Inf. Syst."},{"key":"511_CR45","doi-asserted-by":"crossref","unstructured":"Singla, P., Domingos, P.M.: Entity resolution with markov logic. In: ICDM, pp. 572\u2013582 (2006)","DOI":"10.1109\/ICDM.2006.65"},{"key":"511_CR46","volume-title":"Probabilistic Databases. Synthesis Lectures on Data Management","author":"D Suciu","year":"2011","unstructured":"Suciu, D., Olteanu, D., R\u00e9, C., Koch, C.: Probabilistic Databases. Synthesis Lectures on Data Management. Morgan & Claypool Publishers, San Rafael (2011)"},{"key":"511_CR47","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/3-540-56023-8_3","volume-title":"Entity-Relationship Approach \u2014 ER '92","author":"Bernhard Thalheim","year":"1992","unstructured":"Thalheim, B.: Fundamentals of cardinality constraints. In: ER, pp. 7\u201323 (1992)"},{"key":"511_CR48","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04058-4","volume-title":"Entity-relationship modeling","author":"B Thalheim","year":"2000","unstructured":"Thalheim, B.: Entity-relationship modeling. Springer, Berlin (2000)"},{"key":"511_CR49","first-page":"42","volume-title":"Lecture Notes in Computer Science","author":"Bernhard Thalheim","year":"2011","unstructured":"Thalheim, B.: Integrity constraints in (conceptual) database models. In: The Evolution of Conceptual Modeling, pp. 42\u201367 (2008)"}],"container-title":["The VLDB Journal"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00778-018-0511-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00778-018-0511-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00778-018-0511-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,5]],"date-time":"2025-07-05T13:43:42Z","timestamp":1751723022000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00778-018-0511-z"}},"subtitle":["Validation, Reasoning, and Semantic Summaries"],"short-title":[],"issued":{"date-parts":[[2018,7,2]]},"references-count":49,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["511"],"URL":"https:\/\/doi.org\/10.1007\/s00778-018-0511-z","relation":{},"ISSN":["1066-8888","0949-877X"],"issn-type":[{"type":"print","value":"1066-8888"},{"type":"electronic","value":"0949-877X"}],"subject":[],"published":{"date-parts":[[2018,7,2]]},"assertion":[{"value":"23 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 June 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 June 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 July 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}