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Consistency Checking in Complex Object Database Schemata with Integrity Constraints
July/August 1998 (vol. 10 no. 4)
pp. 576-598

Abstract—Integrity constraints are rules that should guarantee the integrity of a database. Provided an adequate mechanism to express them is available, the following question arises: Is there any way to populate a database which satisfies the constraints supplied by a database designer? That is, does the database schema, including constraints, admit at least a nonempty model? This work answers the above question in a complex object database environment, providing a theoretical framework, including the following ingredients: 1) two alternative formalisms, able to express a relevant set of state integrity constraints with a declarative style; 2) two specialized reasoners, based on the tableaux calculus, able to check the consistency of complex objects database schemata expressed with the two formalisms. The proposed formalisms share a common kernel, which supports complex objects and object identifiers, and which allow the expression of acyclic descriptions of: classes, nested relations and views, built up by means of the recursive use of record, quantified set, and object type constructors and by the intersection, union, and complement operators. Furthermore, the kernel formalism allows the declarative formulation of typing constraints and integrity rules. In order to improve the expressiveness and maintain the decidability of the reasoning activities, we extend the kernel formalism into two alternative directions. The first formalism, ${\cal OLCP,}$ introduces the capability of expressing path relations. Because cyclic schemas are extremely useful, we introduce a second formalism, ${\cal OLCD,}$ with the capability of expressing cyclic descriptions but disallowing the expression of path relations. In fact, we show that the reasoning activity in ${\cal OLCDP}$ (i.e., ${\cal OLCP}$ with cycles) is undecidable.

[1] S. Abiteboul, R. Hull, “IFO: A Formal Semantic Database Model,” ACM Trans. Database Systems, vol. 12, no. 4, pp. 525–565, Dec. 1987.
[2] S. Abiteboul and P.C. Kanellakis,“Object identity as a query language primitive,” Proc. 1989 ACM SIGMOD Int’l Conf. the Management of Data, SIGMOD Record, vol. 18, no. 2, pp. 159-173, June 1989.
[3] LOGIDATA+: Deductive Databases with Complex Objects, P. Atzeni, ed, vol. 701of Lecture Notes in Computer Science, Springer-Verlag, Heidelberg, Germany, 1993.
[4] P. Atzeni and D.S. ParkerJr., “Formal Properties of Net-Based Knowledge Representation Schemes,” Data&Knowledge Eng. 3, pp. 137-147, 1988.
[5] F. Baader and P. Hanschke, "A Scheme for Integrating Concrete Domains into Concept Languages," Proc. 12th Int'l Joint Conf. Artificial Intelligence,Sydney, Australia, 1991.
[6] J.P. Ballerini, D. Beneventano, S. Bergamaschi, C. Sartori, and M. Vincini, "A Semantics Driven Query Optimizer for OODBs," A. Borgida, M. Lenzerini, D. Nardi, and B. Nebel, eds., Proc. DL95: Int'l Workshop Description Logics, vol. 07.95 of Dip. di Informatica e Sistemistica, Univ. di Roma "La Sapienza," Rapp. Tecnico, pp. 59-62,Rome, June 1995.
[7] Building An Object-Oriented Database System: The Story of O2, F. Bancilhon, C. Delobel, and P. Kanelakis, eds. San Mateo, Calif.: Morgan Kaufmann, 1992.
[8] G. Di Battista and M. Lenzerini, “Deductive Entity Relationship Modeling,” IEEE Trans. Knowledge and Data Eng., vol. 5, no. 3, June 1993.
[9] H.W. Beck, S.K. Gala, and S.B. Navathe, Classification as a Query Processing Technique in the CANDIDE Semantic Data Model Proc. First Int'l Conf. Data Eng., pp. 572-581, 1989.
[10] D. Beneventano, S. Bergamaschi, and B. Nebel, "Subsumption for Complex Objects Data Models," Proc. Int'l Conf. Database Theory,Berlin, 1992.
[11] D. Beneventano, S. Bergamaschi, S. Lodi, and C. Sartori, "Using Subsumption in Semantic Query Optimization," A. Napoli, ed., Proc. IJCAI Workshop Object-Based Representation Systems, pp. 19-31, Aug. 1993.
[12] D. Beneventano, S. Bergamaschi, and C. Sartori, "Taxonomic Reasoning with Cycles in LOGIDATA+," P. Atzeni, ed., LOGIDATA+: Deductive Databases with Complex Objects, vol. 701of Lecture Notes in Computer Science, pp. 105-128. Springer-Verlag, Heidelberg, Germany, 1993.
[13] D. Beneventano, S. Bergamaschi, and C. Sartori, "Using Subsumption for Semantic Query Optimization in OODB," Proc. Int'l Workshop Description Logics, vol. D-94-10 of DFKI—Document, pp. 97-100,Bonn, Germany, June 1994.
[14] D. Beneventano, S. Bergamaschi, and C. Sartori, "Semantic Query Optimization by Subsumption in OODB," H. Christiansen, H.L. Larsen, and T. Andreasen, eds., Flexible Query Answering Systems, vol. 62of Datalogiske Skrifter, Roskilde, Denmark, 1996.
[15] S. Bergamaschi and B. Nebel, "The Complexity of Multiple Inheritance in Complex Object Data Models," Proc. IJCAI '91, Workshop AI and Objects,Sydney, Australia, Aug. 1991.
[16] S. Bergamaschi and B. Nebel, "Acquisition and Validation of Complex Object Database Schemata Supporting Multiple Inheritance," J. Applied Intelligence, vol. 4, pp. 185-203, 1994.
[17] S. Bergamaschi and C. Sartoni, “On Taxonomic Reasoning in Conceptual Design,” ACM Trans. Database Systems, vol. 17, no. 3, pp. 385-422, 1992.
[18] E. Bertino and L. Martino,Object-Oriented Database Systems. Int’l Computer Science Series. Addison-Wesley, 1993.
[19] A. Borgida et al., "Classic: A Structural Data Model for Objects," Proc. 1989 ACM SIGMOD Int'l Conf. Management of Data, ACM Press, New York, 1989, pp. 59-67.
[20] R.J. Brachman and J.G. Schmolze, "An Overview of the KL-ONE Knowledge Representation System, Cognitive Science, vol. 9, no. 2, pp. 171-216, 1985.
[21] F. Bry, H. Decker, and R. Manthey, "A Uniform Approach to Constraint Satisfaction and Constraint Satisfiability in Deductive Databases," H.W. Schmidt, S. Ceri, and M. Missikoff, eds., Proc. EDBT '88—Advances in Database Technology, pp. 488-505,Heidelberg, Germany, Springer-Verlag, Mar. 1988.
[22] D. Calvanese and M. Lenzerini, “Making Object-Oriented Schemes More Expressive,” Proc. 13th Int'l Symp. Principles of Database Systems (PODS '94), May 1994.
[23] D. Calvanese, M. Lenzerini, and D. Nardi, "A Unified Framework for Class-Based Formalisms," J. Allen, R. Fikes, and E. Sandewall, eds., Proc. KR '94—Int'l Conf. Principles of Knowledge Representation and Reasoning, pp. 109-120,Cambridge, Mass., Morgan Kaufmann, 1994.
[24] L. Cardelli, "A Semantics of Multiple Inheritance," Semantics of Data Types, pp.51-67. Springer-Verlag, 1984.
[25] N. Coburn and G.E. Weddel, "Path Constraints for Graph-Based Data Models: Towards a Unified Theory of Typing Constraints, Equations and Functional Dependencies," Proc. Second Int'l Conf. Deductive and Object-Oriented Databases, pp. 312-331,Heidelberg, Germany, Springer-Verlag, Dec. 1991.
[26] L. Delcambre and K. Davis,“Automatic validation of object-oriented database structures,” Proc. IEEE Data Eng. Conf.,Los Angeles, pp. 2-9, 1989.
[27] F.M. Donini, M. Lenzerini, D. Nardi, and W. Nutt, "The Complexity of Concept Languages," J. Allen, R. Fikes, and E. Sandewall, eds., Proc. KR '91—Second Int'l Conf. Principles of Knowledge Representation and Reasoning, pp. 151-162,Cambridge, Mass., Morgan Kaufmann, Apr. 1991
[28] F.M. Donini, A. Schaerf, and M. Buchheit, "Decidable Reasoning in Terminological Knowledge Representation Systems," Proc. 13th Int'l Joint Conf. Artificial Inteligence, Sept. 1993.
[29] F.M. Donini, B. Hollunder, M. Lenzerini, A. Marchetti Spaccamela, D. Nardi, and W. Nutt, "The Complexity of Existential Quantification in Concept Languages," Artificial Intelligence, vol. 53, pp. 309-327, 1992.
[30] Proc. ODMG '93—The Object Database Standard, R.G.G. Cattell, ed. Morgan Kaufmann, San Mateo, Calif., 1994.
[31] T. Finin and D. Silverman, "Interactive Classification as a Knowledge Acquisition Tool," L. Kershberg, ed., Expert Database Systems, pp. 79-90, Benjamin/Cummings, 1986.
[32] H. Gallaire and J.M. Nicholas, “Logic and Databases: An Assessment,” Proc. Third Int'l Conf. Database Theory (ICDT '90), S. Abiteboul and P. Kanellakis, eds., 1990.
[33] Y. Gurevich, "The Word Problem for Certain Classes of Semigroups," Algebra and Logic, vol. 5, pp. 25-35, 1966.
[34] P. Hanschke, "Specifying Role Interaction in Concept Languages," B. Nebel, C. Rich, and W. Swartout, eds., Proc. Third Int'l Conf. Principles of Knowledge Representation and Reasoning, pp. 318-329, Morgan Kaufmann, 1992.
[35] B. Hollunder, W. Nutt, and M. Schmidt-Schauss, "Subsumption Algorithms for Concept Description Languages," Proc. Ninth ECAI, pp. 348-353,Stockholm, Sweden, 1990.
[36] M. Kifer, W. Kim, and Y. Sagiv, “Querying Object-Oriented Databases,” Proc. ACM SIGMOD Conf., 1992.
[37] M. Kifer, G. Lausen, and J. Wu, "Logical Foundations of Object-Oriented and Frame-Based Languages," J. ACM, vol. 42, pp. 741-843, 1995.
[38] C. Kung, "A Tableaux Approach for Consistency Checking," Proc. Conf. Theoretical and Formal Aspects of Information Systems, IFIP WG 8.1, Sitges, Spain, Apr. 1985.
[39] C. Lecluse and P. Richard, "Modeling Complex Structures in Object-Oriented Databases," Proc. Symp. Principles of Database Systems, pp. 360-368, 1989.
[40] Z. Manna and N. Dershowitz, "Proving Termination with Multiset Orderings," Comm. ACM, vol. 22, no. 8, pp. 465-476, Aug. 1979.
[41] R. Manthey, "Satisfiability of Integrity Constraints: Reflections on a Neglected Problem," Proc. Int'l Workshop Foundations of Models and Languages for Data and Objects,Aigen, Austria, Sept. 1990.
[42] R. Manthey and F. Bry, “SATCHMO: A Theorem Prover Implemented in Prolog,” Proc. Int'l Conf. Automated Deduction, pp. 415-434, 1988.
[43] B. Nebel, "Terminological Cycles: Semantics and Computational Properties," J.F. Sowa, ed., Principles of Semantic Networks, ch. 11, pp. 331-362, Morgan Kaufmann, San Mateo, Calif., 1991.
[44] E.L. Post, "Recursive Unsolvability of a Problem of Thue," J. Symbolic Logic, vol. 12, pp. 1-11, 1947.
[45] D.J. Rosenkrantz and H.B. Hunt, "Processing Conjunctive Predicates and Queries," Proc. Int'l Conf. Very Large Data Bases, pp. 64-72,Montreal, Oct. 1980.
[46] M. Schmidt-Schauß and G. Smolka, "Attributive Concept Descriptions with Complements," Artificial Intelligence, Vol. 48, No. 1, 1991, pp. 1-26.
[47] R.M. Smullyan, First-Order Logic, Springer-Verlag, Berlin, 1986.
[48] Principles of Semantic Networks, J. Sowa, ed., Morgan Kaufmann, San Mateo, Calif., 1991.
[49] M. Stonebraker, Object Relational DBMSs, Morgan Kaufmann, San Mateo, Calif., 1994.
[50] M.F. van Bommel and G.E. Weddell, Reasoning about Equations and Functional Dependencies on Complex Objects IEEE Trans. Knowledge and Data Eng., vol. 6, no. 3, pp. 455-469, 1994.
[51] G.E. Weddell, Reasoning about Functional Dependencies Generalized for Semantic Data Models ACM Trans. Database Systems, vol. 17, no. 1, pp. 32-64, Mar. 1992.

Index Terms:
Database models, database semantics, consistency checking, complex object models, description logics, integrity constraints, object-oriented database, semantic integrity, subsumption.
Domenico Beneventano, Sonia Bergamaschi, Stefano Lodi, Claudio Sartori, "Consistency Checking in Complex Object Database Schemata with Integrity Constraints," IEEE Transactions on Knowledge and Data Engineering, vol. 10, no. 4, pp. 576-598, July-Aug. 1998, doi:10.1109/69.706058
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