Measure-Based Inconsistency-Tolerant Maintenance of Database Integrity

[EN] To maintain integrity, constraint violations should be prevented or repaired. However, it may not be feasible to avoid inconsistency, or to repair all violations at once. Based on an abstract concept of violation measures, updates and repairs can be checked for keeping inconsistency bounded, such that integrity violations are guaranteed to never get out of control. This measure-based approach goes beyond conventional methods that are not meant to be applied in the presence of inconsistency. It also generalizes recently introduced concepts of inconsistency-tolerant integrity maintenance.Partially supported by FEDER and the Spanish grants TIN2009-14460-C03 and TIN2010-17139Decker, H. (2013). Measure-Based Inconsistency-Tolerant Maintenance of Database Integrity. Lecture Notes in Computer Science. 7693:149-173. https://doi.org/10.1007/978-3-642-36008-4_7S1491737693Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)Abiteboul, S., Vianu, V.: A transaction-based approach to relational database specification. JACM 36(4), 758–789 (1989)Afrati, F., Kolaitis, P.: Repair checking in inconsistent databases: algorithms and complexity. In: 12th ICDT, pp. 31–41. ACM Press (2009)Arenas, M., Bertossi, L., Chomicki, J.: Consistent query answers in inconsistent databases. In: PODS 1999, pp. 68–79. ACM Press (1999)Arieli, O., Denecker, M., Bruynooghe, M.: Distance semantics for database repair. Ann. Math. Artif. Intell. 50, 389–415 (2007)Arni-Bloch, N., Ralyté, J., Léonard, M.: Service–Driven Information Systems Evolution: Handling Integrity Constraints Consistency. In: Persson, A., Stirna, J. (eds.) PoEM 2009. LNBIP, vol. 39, pp. 191–206. Springer, Heidelberg (2009)Bauer, H.: Maß- und Integrationstheorie, 2. Auflage. De Gruyter (1992)Besnard, P., Hunter, A.: Quasi-Classical Logic: Non-Trivializable Classical Reasoning from Inconsistent Information. In: Froidevaux, C., Kohlas, J. (eds.) ECSQARU 1995. LNCS, vol. 946, pp. 44–51. Springer, Heidelberg (1995)Bohanon, P., Fan, W., Flaster, M., Rastogi, R.: A Cost-Based Model and Effective Heuristic for Repairing Constraints by Value Modification. In: Proc. SIGMOD 2005, pp. 143–154. ACM Press (2005)Ceri, S., Cochrane, R., Widom, J.: Practical Applications of Triggers and Constraints: Success and Lingering Issues. In: Proc. 26th VLDB, pp. 254–262. Morgan Kaufmann (2000)Chakravarthy, U., Grant, J., Minker, J.: Logic-based Approach to Semantic Query Optimization. Transactions on Database Systems 15(2), 162–207 (1990)Chomicki, J.: Consistent Query Answering: Five Easy Pieces. In: Schwentick, T., Suciu, D. (eds.) ICDT 2007. LNCS, vol. 4353, pp. 1–17. Springer, Heidelberg (2006)Christiansen, H., Martinenghi, D.: On simplification of database integrity constraints. Fundamenta Informaticae 71(4), 371–417 (2006)Clark, K.: Negation as Failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press (1978)Curino, C., Moon, H., Deutsch, A., Zaniolo, C.: Update Rewriting and Integrity Constraint Maintenance in a Schema Evolution Support System: PRISM++. PVLDB 4, 117–128 (2010)Dawson, J.: The compactness of first-order logic: From Gödel to Lindström. History and Philosophy of Logic 14(1), 15–37 (1993)Decker, H.: The Range Form of Databases and Queries or: How to Avoid Floundering. In: Proc. 5th ÖGAI. Informatik-Fachberichte, vol. 208, pp. 114–123. Springer (1989)Decker, H.: Drawing Updates From Derivations. In: Kanellakis, P.C., Abiteboul, S. (eds.) ICDT 1990. LNCS, vol. 470, pp. 437–451. Springer, Heidelberg (1990)Decker, H.: Extending Inconsistency-Tolerant Integrity Checking by Semantic Query Optimization. In: Bhowmick, S.S., Küng, J., Wagner, R. (eds.) DEXA 2008. LNCS, vol. 5181, pp. 89–96. Springer, Heidelberg (2008)Decker, H.: Answers That Have Integrity. In: Schewe, K.-D., Thalheim, B. (eds.) SDKB 2010. LNCS, vol. 6834, pp. 54–72. Springer, Heidelberg (2011)Decker, H.: Causes of the Violation of Integrity Constraints for Supporting the Quality of Databases. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part V. LNCS, vol. 6786, pp. 283–292. Springer, Heidelberg (2011)Decker, H.: Inconsistency-tolerant Integrity Checking based on Inconsistency Metrics. In: König, A., Dengel, A., Hinkelmann, K., Kise, K., Howlett, R.J., Jain, L.C. (eds.) KES 2011, Part II. LNCS, vol. 6882, pp. 548–558. Springer, Heidelberg (2011)Decker, H.: Partial Repairs that Tolerate Inconsistency. In: Eder, J., Bielikova, M., Tjoa, A.M. (eds.) ADBIS 2011. LNCS, vol. 6909, pp. 389–400. Springer, Heidelberg (2011)Decker, H.: Consistent Explanations of Answers to Queries in Inconsistent Knowledge Bases. In: Roth-Berghofer, T., Tintarev, N., Leake, D. (eds.) Explanation-aware Computing, Proc. IJCAI 2011 Workshop ExaCt 2011, pp. 71–80 (2011), http://exact2011.workshop.hm/index.phpDecker, H., Martinenghi, D.: Classifying integrity checking methods with regard to inconsistency tolerance. In: Proc. PPDP 2008, pp. 195–204. ACM Press (2008)Decker, H., Martinenghi, D.: Modeling, Measuring and Monitoring the Quality of Information. In: Heuser, C.A., Pernul, G. (eds.) ER 2009. LNCS, vol. 5833, pp. 212–221. Springer, Heidelberg (2009)Decker, H., Martinenghi, D.: Inconsistency-tolerant Integrity Checking. IEEE TKDE 23(2), 218–234 (2011)Decker, H., Muñoz-Escoí, F.D.: Revisiting and Improving a Result on Integrity Preservation by Concurrent Transactions. In: Meersman, R., Dillon, T., Herrero, P. (eds.) OTM 2010 Workshops. LNCS, vol. 6428, pp. 297–306. Springer, Heidelberg (2010)Dung, P., Kowalski, R., Toni, F.: Dialectic Proof Procedures for Assumption-based Admissible Argumentation. Artificial Intelligence 170(2), 114–159 (2006)Ebbinghaus, H.-D., Flum, J.: Finite Model Theory, 2nd edn. Springer (2006)Embury, S., Brandt, S., Robinson, J., Sutherland, I., Bisby, F., Gray, A., Jones, A., White, R.: Adapting integrity enforcement techniques for data reconciliation. Information Systems 26, 657–689 (2001)Enderton, H.: A Mathematical Introduction to Logic, 2nd edn. Academic Press (2001)Eiter, T., Fink, M., Greco, G., Lembo, D.: Repair localization for query answering from inconsistent databases. ACM TODS 33(2), article 10 (2008)Furfaro, F., Greco, S., Molinaro, C.: A three-valued semantics for querying and repairing inconsistent databases. Ann. Math. Artif. Intell. 51(2-4), 167–193 (2007)Grant, J., Hunter, A.: Measuring the Good and the Bad in Inconsistent Information. In: Proc. 22nd IJCAI, pp. 2632–2637 (2011)Greco, G., Greco, S., Zumpano, E.: A logical framework for querying and repairing inconsistent databases. 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AAAI Press (2008)Hunter, A., Konieczny, S.: On the measure of conflicts: Shapley Inconsistency Values. Artificial Intelligence 174, 1007–1026 (2010)Kakas, A., Mancarella, P.: Database updates through abduction. In: Proc. 16th VLDB, pp. 650–661. Morgan Kaufmann (1990)Kakas, A., Kowalski, R., Toni, F.: The role of Abduction in Logic Programming. In: Gabbay, D., Hogger, C., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 5, pp. 235–324. Oxford University Press (1998)Lee, S.Y., Ling, T.W.: Further improvements on integrity constraint checking for stratifiable deductive databases. In: Proc. VLDB 1996, pp. 495–505. Morgan Kaufmann (1996)Lehrer, K.: Relevant Deduction and Minimally Inconsistent Sets. Journal of Philosophy 3(2,3), 153–165 (1973)Mu, K., Liu, W., Jin, Z., Bell, D.: A Syntax-based Approach to Measuring the Degree of Inconsistency for Belief Bases. J. Approx. Reasoning 52(7), 978–999 (2011)Lloyd, J., Sonenberg, L., Topor, R.: Integrity constraint checking in stratified databases. J. Logic Programming 4(4), 331–343 (1987)Lozinskii, E.: Resolving contradictions: A plausible semantics for inconsistent systems. J. Automated Reasoning 12(1), 1–31 (1994)Ma, Y., Qi, G., Hitzler, P.: Computing inconsistency measure based on paraconsistent semantics. J. Logic Computation 21(6), 1257–1281 (2011)Martinenghi, D., Christiansen, H.: Transaction Management with Integrity Checking. In: Andersen, K.V., Debenham, J., Wagner, R. (eds.) DEXA 2005. LNCS, vol. 3588, pp. 606–615. Springer, Heidelberg (2005)Martinenghi, D., Christiansen, H., Decker, H.: Integrity Checking and Maintenance in Relational and Deductive Databases and Beyond. In: Ma, Z. (ed.) Intelligent Databases: Technologies and Applications, pp. 238–285. IGI Global (2006)Martinez, M.V., Pugliese, A., Simari, G.I., Subrahmanian, V.S., Prade, H.: How Dirty Is Your Relational Database? An Axiomatic Approach. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 103–114. Springer, Heidelberg (2007)Meyer, J., Wieringa, R. (eds.): Deontic Logic in Computer Science. Wiley (1994)Nicolas, J.M.: Logic for improving integrity checking in relational data bases. Acta Informatica 18, 227–253 (1982)Plexousakis, D., Mylopoulos, J.: Accommodating Integrity Constraints During Database Design. In: Apers, P.M.G., Bouzeghoub, M., Gardarin, G. (eds.) EDBT 1996. LNCS, vol. 1057, pp. 495–513. Springer, Heidelberg (1996)Rahm, E., Do, H.: Data Cleaning: Problems and Current Approaches. Data Engineering Bulletin 23(4), 3–13 (2000)Sadri, F., Kowalski, R.: A theorem-proving approach to database integrity. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 313–362. Morgan Kaufmann (1988)Thimm, M.: Measuring Inconsistency in Probabilistic Knowledge Bases. In: Proc. 25th UAI, pp. 530–537. AUAI Press (2009)Vardi, M.: On the integrity of databases with incomplete information. In: Proc. 5th PODS, pp. 252–266. ACM Press (1986)Wijsen, J.: Database repairing using updates. ACM Trans. Database Syst. 30(3), 722–768 (2005

Minimizing Risks of Decision Making by Inconsistency-Tolerant Integrity Management

[EN] In practice, knowledge-based reasoning for decision making must be inconsistency-tolerant since, for decision making, contradictory data are unavoidable. We present a measure-based concept of inconsistency-tolerant knowledge engineering for decision support. It enables the preservation of consistency across updates, as well as the computation of sound answers to queries in knowledge bases with violated integrity. Hence, our framework supports the consistency of decision making in the presence of contradictory data. By an extended example, we show how inconsistency-tolerant integrity maintenance can minimize risks in decision making that result from inconsistent knowledge.Supported by ERDF/FEDER and MECgrants TIN2009-14460-C03, TIN2010-17139, TIN2012-37719-C03-01.Decker, H. (2013). Minimizing Risks of Decision Making by Inconsistency-Tolerant Integrity Management. Lecture Notes in Computer Science. 8186:556-565. https://doi.org/10.1007/978-3-642-41033-8_70S5565658186Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)Arenas, M., Bertossi, L., Chomicki, J.: Consistent query answers in inconsistent databases. In: Proc. 18th PODS, pp. 68–79. ACM Press (1999)Bertossi, L., Hunter, A., Schaub, T. (eds.): Inconsistency Tolerance. LNCS, vol. 3300. Springer, Heidelberg (2005)Carnielli, W., Coniglio, M., D’Ottaviano, I. (eds.): The Many Sides of Logic. Studies in Logic, vol. 21. College Publications, London (2009)Ceri, S., Cochrane, R., Widom, J.: Practical Applications of Triggers and Constraints: Success and Lingering Issues. In: 26th VLDB, pp. 254–262. Morgan Kaufmann (2000)Chakravarthy, U., Grant, J., Minker, J.: Logic-based approach to semantic query optimization. Transactions on Database Systems 15(2), 162–207 (1990)Chomicki, J.: Consistent query answering: Five easy pieces. In: Schwentick, T., Suciu, D. (eds.) ICDT 2007. LNCS, vol. 4353, pp. 1–17. Springer, Heidelberg (2006)Clark, K.: Negation as Failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press (1978)Decker, H.: Answers That Have Integrity. In: Schewe, K.-D. (ed.) SDKB 2010. LNCS, vol. 6834, pp. 54–72. Springer, Heidelberg (2011)Decker, H.: Measure-Based Inconsistency-Tolerant Maintenance of Database Integrity. In: Schewe, K.-D., Thalheim, B. (eds.) SDKB 2013. LNCS, vol. 7693, pp. 149–173. Springer, Heidelberg (2013)Decker, H., Martinenghi, D.: Inconsistency-tolerant Integrity Checking. TKDE 23(2), 218–234 (2011)Fung, T.H., Kowalski, R.: The IFF proof procedure for abductive logic programming. J. Logic Programming 33(2), 151–165 (1997)Fuxmann, A., Miller, R.: Towards Inconsistency Management in Data Integration Systems. In: Proc. IJCAI 2003 Workshop IIWEB, pp. 143–148 (2003)Gupta, A., Sagiv, Y., Ullman, J., Widom, J.: Constraint checking with partial information. In: Proc. 13th PODS, pp. 45–55. ACM Press (1994)Hunter, A., Konieczny, S.: Approaches to measuring inconsistent information. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol. 3300, pp. 191–236. Springer, Heidelberg (2005)Lee, S.Y., Ling, T.W.: Further improvements on integrity constraint checking for stratifiable deductive databases. In: 22th International Conference on Very Large Data Bases, pp. 495–505. Morgan Kaufmann (1996)Motro, A., Smets, P.: Uncertainty Management in Information Systems: From Needs to Solutions. Kluwer (1996)Restall, G.: Laws of Non-contradiction, Laws of Excluded Middle and Logics. In: Priest, G., et al. (eds.) The Law of Non-Contradiction - New Philosophical Essays, pp. 73–85. Oxford University Press (2004

Maintaining Desirable Properties of Information by Inconsistency-Tolerant Integrity Management

[EN] We argue that several kinds of desirable semantic properties of data provided by information systems, such as their quality, trustworthiness, certainty, security or lack of riskiness, can be modeled and maintained by existing database integrity technology. As opposed to the usual requirement for conventional integrity constraints, formulas that model such properties may not always be perfectly satisfied. Therefore, it is necessary to be less rigorous about the satisfaction of such properties. That can be achieved by recently introduced techniques of inconsistency tolerance, in the fields of integrity checking, integrity repair and query answering. We support our argument by an extended example. Guardar / Salir Siguiente >Decker ., H. (2013). Maintaining Desirable Properties of Information by Inconsistency-Tolerant Integrity Management. Lecture Notes in Business Information Processing. 137:13-24. doi:10.1007/978-3-642-38370-0_2S1324137Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)Arenas, M., Bertossi, L., Chomicki, J.: Consistent query answers in inconsistent databases. In: 18th Symposium on Principles of Database Systems, pp. 68–79. ACM Press (1999)Bertossi, L., Hunter, A., Schaub, T. (eds.): Inconsistency Tolerance. LNCS, vol. 3300. Springer, Heidelberg (2005)Bowen, K., Kowalski, R.: Amalgamating Language and Metalanguage. In: Clark, K., Tärnlund, S.-A. (eds.) Logic Programming, pp. 153–172. Academic Press (1982)Carnielli, W., Coniglio, M., D’Ottaviano, I. (eds.): The Many Sides of Logic. Studies in Logic, vol. 21. College Publications, London (2009)Ceri, S., Cochrane, R., Widom, J.: Practical Applications of Triggers and Constraints: Success and Lingering Issues. In: 26th VLDB, pp. 254–262. Morgan Kaufmann (2000)Chakravarthy, U., Grant, J., Minker, J.: Logic-based approach to semantic query optimization. Transactions on Database Systems 15(2), 162–207 (1990)Clark, K.: Negation as Failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press (1978)Decker, H.: The Range Form of Databases and Queries or: How to Avoid Floundering. In: 5th ÖGAI. Informatik-Fachberichte., vol. 208, pp. 114–123. Springer, Heidelberg (1989)Decker, H.: Answers that Have Integrity. In: Schewe, K.-D. (ed.) SDKB 2010. LNCS, vol. 6834, pp. 54–72. Springer, Heidelberg (2011)Decker, H.: Measure-based Inconsistency-tolerant Maintenance of Database Integrity. In: Schewe, K.-D., Thalheim, B. (eds.) SDKB 2013. LNCS, vol. 7693, pp. 149–173. Springer, Heidelberg (2013)Decker, H.: Partial Repairs that Tolerate Inconsistency. In: Eder, J., Bielikova, M., Tjoa, A.M. (eds.) ADBIS 2011. LNCS, vol. 6909, pp. 389–400. Springer, Heidelberg (2011)Decker, H., Martinenghi, D.: Modeling, Measuring and Monitoring the Quality of Information. In: Heuser, C.A., Pernul, G. (eds.) ER 2009. LNCS, vol. 5833, pp. 212–221. Springer, Heidelberg (2009)Decker, H., Martinenghi, D.: Inconsistency-tolerant Integrity Checking. TKDE 23(2), 218–234 (2011)Fung, T.H., Kowalski, R.: The IFF proof procedure for abductive logic programming. J. Logic Programming 33(2), 151–165 (1997)Gupta, A., Sagiv, Y., Ullman, J., Widom, J.: Constraint checking with partial information. In: 13th Symposium on Principles of Database Systems, pp. 45–55. ACM Press (1994)Hunter, A., Konieczny, S.: Approaches to measuring inconsistent information. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol. 3300, pp. 191–236. Springer, Heidelberg (2005)Lee, S.Y., Ling, T.W.: Further improvements on integrity constraint checking for stratifiable deductive databases. In: 22th International Conference on Very Large Data Bases, pp. 495–505. Morgan Kaufmann (1996)Motro, A., Smets, P.: Uncertainty Management in Information Systems: From Needs to Solutions. Kluwer (1996)Schewe, K.D., Thalheim, B.: Limitations of Rule Triggering Systems for Integrity Maintenance in the Context of Transition Specifications. Acta Cybernetica 13(3), 277–304 (1998

Partial Repairs that Tolerate Inconsistency

[EN] The consistency of databases can be supported by enforcing integrity constraints on the stored data. Constraints that are violated should be repaired by eliminating the causes of the violations. Traditionally, repairs are conceived to be total. However, it may be unfeasible to eliminate all violations. We show that it is possible to get by with partial repairs that tolerate extant inconsistencies. They may not eliminate all causes of integrity violations but preserve the consistent parts of the database. Remaining violations can be controlled by measuring inconsistency, and further reduced by inconsistency-tolerant integrity checking.Partially supported by FEDER and the Spanish grants TIN2009-14460-C03 and TIN2010-17139.Decker, H. (2011). Partial Repairs that Tolerate Inconsistency. Lecture Notes in Computer Science. 6909:389-400. https://doi.org/10.1007/978-3-642-23737-9_283894006909Afrati, F., Kolaitis, P.: Repair checking in inconsistent databases: algorithms and complexity. In: 12th ICDT, pp. 31–41. ACM Press, New York (2009)Arenas, M., Bertossi, L., Chomicki, J.: Consistent query answers in inconsistent databases. In: PODS 1999, pp. 68–79. ACM Press, New York (1999)Caroprese, L., Greco, S., Zumpano, E.: Active Integrity Constraints for Database Consistency Maintenance. IEEE TKDE 21(7), 1042–1057 (2009)Caroprese, L., Truszczynski, M.: Active Integrity Constraints and Revision Programming. To appear in TPLP (2010), http://arxiv.org/abs/1009.2270Ceri, S., Cochrane, R., Widom, J.: Practical Applications of Triggers and Constraints: Success and Lingering Issues (10-Year Award). In: Proc. 26th VLDB, pp. 254–262. Morgan Kaufmann, San Francisco (2000)Chomicki, J.: Consistent query answering: Five easy pieces. In: Schwentick, T., Suciu, D. (eds.) ICDT 2007. LNCS, vol. 4353, pp. 1–17. Springer, Heidelberg (2006)Christiansen, H., Martinenghi, D.: On simplification of database integrity constraints. Fundamenta Informaticae 71(4), 371–417 (2006)Decker, H.: Drawing Updates From Derivations. In: Kanellakis, P.C., Abiteboul, S. (eds.) ICDT 1990. LNCS, vol. 470, pp. 437–451. Springer, Heidelberg (1990)Decker, H.: Toward a Uniform Cause-based Approach to Inconsistency-tolerant Database Semantics. In: Meersman, R., Dillon, T., Herrero, P. (eds.) OTM 2010. LNCS, vol. 6427, pp. 983–998. Springer, Heidelberg (2010)Decker, H., Martinenghi, D.: Modeling, Measuring and Monitoring the Quality of Information. In: Heuser, C.A., Pernul, G. (eds.) ER 2009. LNCS, vol. 5833, pp. 212–221. Springer, Heidelberg (2009)Decker, H., Martinenghi, D.: Inconsistency-tolerant Integrity Checking. IEEE TKDE 23(2), 218–234 (2011)Dung, P.M., Kowalski, R., Toni, F.: Dialectic proof procedures for assumption-based admissible argumentation. Artificial Intelligence 170(2), 114–159 (2006)Eiter, T., Fink, M., Greco, G., Lembo, D.: Repair localization for query answering from inconsistent databases. ACM TODS 33(2) (2008)Furfaro, F., Greco, S., Molinaro, C.: A three-valued semantics for querying and repairing inconsistent databases. Ann. Math. Artif. Intell. 51(2-4), 167–193 (2007)Greco, G., Greco, S., Zumpano, E.: A logical framework for querying and repairing inconsistent databases. IEEE TKDE 15(6), 1389–1408 (2003)Guessoum, A., Lloyd, J.: Updating knowledge bases. New Generation Computing 8(1), 71–89 (1990)Guessoum, A., Lloyd, J.: Updating knowledge bases II. New Generation Computing 10(1), 73–100 (1991)Gupta, A., Sagiv, Y., Ullman, J., Widom, J.: Constraint checking with partial information. In: Proc. PODS 1994, pp. 45–55. ACM Press, New York (1994)Kakas, A., Mancarella, P.: Database updates through abduction. In: Proc. 16th VLDB, pp. 650–661. Morgan Kaufmann, San Francisco (1990)Kakas, A., Kowalski, R., Toni, F.: The role of Abduction in Logic Programming. In: Handbook in Artificial Intelligence and Logic Programming, pp. 235–324 (1998)Lee, S.Y., Ling, T.W.: Further improvements on integrity constraint checking for stratifiable deductive databases. In: Proc. VLDB 1996, pp. 495–505. Morgan Kaufmann, San Francisco (1996)Lloyd, J., Sonenberg, L., Topor, R.: Integrity constraint checking in stratified databases. J. Logic Programming 4(4), 331–343 (1987)Nicolas, J.M.: Logic for improving integrity checking in relational data bases. Acta Informatica 18, 227–253 (1982)Ramakrishnan, R., Gehrke, J.: Database Management Systems. McGraw-Hill, New York (2003)Sadri, F., Kowalski, R.: A theorem-proving approach to database integrity. In: Foundations of Deductive Databases and Logic Programming, pp. 313–362. Morgan Kaufmann, San Francisco (1988

Managing uncertainty in databases and scaling it up to concurrent transactions

Uncertainty and data integrity are closely related. The uncertainty of data can be modeled and maintained by existing database integrity technology. The usual requirement that integrity constraints must always be satisfied needs to be renounced for constraints that model uncertainty. That is possible due to the recently introduced inconsistency tolerance of methods for integrity checking, integrity repair and query answering. Inconsistency tolerance also enables the scaling up of uncertainty management to concurrent transactions.Cuzzocrea, A.; Juan Marín, RD.; Decker, H.; Muñoz Escoí, FD. (2012). Managing uncertainty in databases and scaling it up to concurrent transactions. En Scalable Uncertainty Management. Springer Verlag (Germany). 7520:30-43. doi:10.1007/978-3-642-33362-0_3S30437520Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)Afrati, F., Kolaitis, P.: Repair Checking in Inconsistent Databases: Algorithms and Complexity. In: ICDT 2009. 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