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Active Integrity Constraints for Database Consistency Maintenance
July 2009 (vol. 21 no. 7)
pp. 1042-1058
Luciano Caroprese, University of Calabria, Italy
Sergio Greco, University of Calabria, Italy
Ester Zumpano, University of Calabria, Italy
This paper introduces active integrity constraints (AICs), an extension of integrity constraints for consistent database maintenance. An active integrity constraint is a special constraint whose body contains a conjunction of literals which must be false and whose head contains a disjunction of update actions representing actions (insertions and deletions of tuples) to be performed if the constraint is not satisfied (that is its body is true). The AICs work in a domino-like manner as the satisfaction of one AIC may trigger the violation and therefore the activation of another one. The paper also introduces founded repairs, which are minimal sets of update actions that make the database consistent, and are specified and “supported” by active integrity constraints. The paper presents: 1) a formal declarative semantics allowing the computation of founded repairs and 2) a characterization of this semantics obtained by rewriting active integrity constraints into disjunctive logic rules, so that founded repairs can be derived from the answer sets of the derived logic program. Finally, the paper studies the computational complexity of computing founded repairs.

[1] S. Abiteboul, R. Hull, and V. Vianu, Foundations of Databases. Addison-Wesley Publishing Co., 1995.
[2] J.J. Alferes, J.A. Leite, L.M. Pereira, H. Przymusinska, and T.C. Przymusinski, “Dynamic Updates of Non-Monotonic Knowledge Bases,” J. Logic Programming, vol. 45, nos.1-3, pp.43-70, 2000.
[3] J.J. Alferes, L.M. Pereira, H. Przymusinska, and T.C. Przymusinski, “Lupsa Language for Updating Logic Programs,” J. Logic Programming, vol. 138, nos.1/2, pp.87-116, 2002.
[4] M. Arenas, L. Bertossi, and J. Chomicki, “Specifying and Querying Database Repairs Using Logic Programs with Exceptions,” Proc. Int'l Conf. Flexible Query Answering, pp.27-41, 2000.
[5] M. Arenas, L.E. Bertossi, and J. Chomicki, “Consistent Query Answers in Inconsistent Databases,” Proc. 18th ACM SIGMOD-SIGACT-SIGART Symp. Principles of Database Systems, pp.68-79, 1999.
[6] C. Baral, “Embedding Revision Programs in Logic Programming Situation Calculus,” J. Logic Programming, vol. 30, no. 1, pp.83-97, 1997.
[7] C. Baral and Y. Zhang, “On the Semantics of Knowledge Update,” Proc. 17th Int'l Joint Conf. Artificial Intelligence, pp.97-102, 2001.
[8] L. Bertossi and J. Pinto, “Specifying Active Rules for Database Maintenance,” Proc. Eighth Int'l Workshop Foundations of Models and Languages for Data and Objects, pp.112-119, 2000.
[9] L. Caroprese, S. Greco, C. Sirangelo, and E. Zumpano, “Declarative Semantics of Production Rules for Integrity Maintenance,” Proc. 22nd Int'l Conf. Logic Programming, pp.26-40, 2006.
[10] S. Ceri, P. Fraternali, S. Paraboschi, and L. Tanca, “Automatic Generation of Production Rules for Integrity Maintenance,” ACM Trans. Database Systems, vol. 19, no. 3, pp.367-422, 1994.
[11] S. Ceri and J. Widom, “Deriving Production Rules for Constraint Maintenance,” Proc. 16th Int'l Conf. Database Theory, pp.566-577, 1990.
[12] J. Chomicki, “Consistent Query Answering: Five Easy Pieces,” Proc. Int'l Conf. Database Theory, pp.1-12, 2007.
[13] J. Chomicki, J. Lobo, and S. Naqvi, “Conflict Resolution Using Logic Programming,” IEEE Trans. Knowledge and Data Eng., vol. 15, no. 1, pp.244-249, Jan./Feb. 2003.
[14] J. Chomicki and J. Marcinkowski, “Minimal-Change Integrity Maintenance Using Tuple Deletions,” Information Computation, vol. 197, nos.1/2, pp.90-121, 2005.
[15] J. Chomicki, J. Marcinkowski, and S. Staworko, “Computing Consistent Query Answers Using Conflict Hypergraphs,” Proc. 13th ACM Int'l Conf. Information and Knowledge Management, pp.417-426, 2004.
[16] T. Eiter and G. Gottlob, “The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revision,” J. Computer and System Sciences vol. 53, no. 3, pp.497-512, 1996.
[17] T. Eiter, G. Gottlob, and H. Mannila, “Disjunctive Data-Log,” ACM Trans. Database Systems, vol. 22, no. 3, pp.364-418, 1997.
[18] M. Fitting, “Annotated Revision Specification Programs,” Proc. Int'l Conf. Logic Programming and Nonmonotonic Reasoning, pp.143-155, 1995.
[19] M. Gelfond and V. Lifschitz, “The Stable Model Semantics for Logic Programming,” Proc. Fifth Int'l Conf. Logic Programming, pp.1070-1080, 1988.
[20] M. Gelfond and V. Lifschitz, “Classical Negation in Logic Programs and Disjunctive Databases,” New Generation Computing, vol. 9, nos.3/4, pp.365-386, 1991.
[21] J. Grant and V.S. Subrahmanian, “Reasoning in Inconsistent Knowledge Bases,” IEEE Trans. Knowledge and Data Eng., vol. 7, no. 1, pp.177-189, Feb. 1995.
[22] G. Greco, S. Greco, and E. Zumpano, “A Logical Framework for Querying and Repairing Inconsistent Databases,” IEEE Trans. Knowledge and Data Eng., vol. 15, no. 6, pp.1389-1408, Nov./Dec. 2003.
[23] S. Greco and E. Zumpano, “Querying Inconsistent Databases,” Proc. Int'l Conf. Logic for Programming and Automated Reasoning, pp.308-325, 2000.
[24] A. Herzig and O. Rifi, “Propositional Belief Base Update and Minimal Change,” Artificial Intelligence, vol. 115, no. 1, pp.107-138, 1999.
[25] H. Katsuno and A.O. Mendelzon, “Propositional Knowledge Base Revision and Minimal Change,” Artificial Intelligence, vol. 52, no. 3, pp.263-294, 1991.
[26] M. Kifer and A. Li, “On the Semantics of Rule-Based Expert Systems with Uncertainty,” Proc. Second Int'l Conf. Database Theory, pp.102-117, 1998.
[27] P. Liberatore, “The Complexity of Belief Update,” Artificial Intelligence, vol. 119, nos.1/2, pp.141-190, 2000.
[28] V. Lifschitz and T. Woo, “Answer Sets in General Nonmonotonic Nonmonotonic Reasoning,” Proc. Third Int'l Conf. Principles of Knowledge Representation and Reasoning, pp.603-614, 1992.
[29] J. Lin, “A Semantics for Reasoning Consistently in the Presence of Inconsistency,” Artificial Intelligence, vol. 86, no. 1, pp.75-95, 1996.
[30] V. Marek, I. Pivkina, and M. Truszczyński, “Annotated Revision Programs,” Artificial Intelligence, vol. 138, nos.1/2, pp.149-180, 2002.
[31] V.W. Marek and M. Truszczyński, “Revision Programming,” Theoretical Computer Science, vol. 190, no. 2, pp.241-277, 1998.
[32] M.V. Martinez, A. Pugliese, G.I. Simari, V.S. Subrahmanian, and H. Prade, “How Dirty Is Your Relational Database? An Axiomatic Approach,” Proc. Ninth European Conf. Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp.103-114, 2007.
[33] C.B. Medeiros and M.J. Andrade, “Implementing Integrity Control in Active Databases,” J. Systems and Software, vol. 27, no. 1, pp.171-181, 1994.
[34] V.S. Subrahmanian, “Amalgamating Knowledge Bases,” ACM Trans. Database Systems, vol. 19, no. 2, pp.291-331, 1994.
[35] V.S. Subrahmanian and L. Amgoud, “A General Framework for Reasoning about Inconsistency,” Proc. 20th Int'l Joint Conf. Artificial Intelligence, pp.599-504, 2007.
[36] J.D. Ullman, Principles of Database and Knowledge-Base Systems, vols.1/2. Computer Science Press, 1998.
[37] J. Wijsen, “Database Repairing Using Updates,” ACM Trans. Database Systems, vol. 30, no. 3, pp.722-768, 2005.
[38] M. Winslett, Updating Logical Databases. Cambridge Univ. Press, 1990.

Index Terms:
Database semantics, inconsistent databases, database repairs, consistent query answering.
Luciano Caroprese, Sergio Greco, Ester Zumpano, "Active Integrity Constraints for Database Consistency Maintenance," IEEE Transactions on Knowledge and Data Engineering, vol. 21, no. 7, pp. 1042-1058, July 2009, doi:10.1109/TKDE.2008.226
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