Reasoning over Extended ER Models
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We investigate the computational complexity of reasoning over various fragments of the Extended Entity-Relationship (EER) language, which includes a number of constructs: isa between entities and relationships, disjointness and covering of entities and relationships, cardinality constraints for entities in relationships and their refinements as well as multiplicity constraints for attributes. We extend the known ExpTime-completeness result for UML class diagrams  and show that reasoning over EER diagrams with isa between relationships is ExpTime-complete even without relationship covering. Surprisingly, reasoning becomes NP-complete when we drop isa between relationships (while still allowing all types of constraints on entities). If we further omit disjointness and covering over entities, reasoning becomes polynomial. Our lower complexity bound results are proved by direct reductions, while the upper bounds follow from the correspondences with expressive variants of the description logic DL-Lite, which we establish in this paper. These correspondences also show the usefulness of DL-Lite as a language for reasoning over conceptual models and ontologies.
KeywordsDescription Logic Conceptual Schema Cardinality Constraint Reachability Problem Reasoning Problem
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- 1.Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: DL-Lite in the light of first-order logic. In: Proc. of the 22nd Nat.Conf. on Artificial Intelligence (AAAI 2007) (2007)Google Scholar
- 3.Batini, C., Ceri, S., Navathe, S.B.: Conceptual Database Design, an Entity-Relationship Approach. Benjamin and Cummings Publ. Co. (1992)Google Scholar
- 4.Bechhofer, S., van Harmelen, F., Hendler, J., Horrocks, I., McGuinness, D.L., Patel-Schneider, P.F., Stein, L.A.: OWL Web Ontology Language reference. W3C Recommendation, Available at (February 2004), http://www.w3.org/TR/owl-ref/
- 7.Calvanese, G.D., Giacomo, D.: Expressive description logics. In: Baader. F., et al. (eds.) , ch.5, pp. 178–218 (2003)Google Scholar
- 8.Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable description logics for ontologies. In: Proc. of the 20th Nat. Conf. on Artificial Intelligence (AAAI 2005), pp. 602–607 (2005)Google Scholar
- 9.Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: Proc. of the 10th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR 2006), pp. 260–270 (2006)Google Scholar
- 10.Calvanese, D., Lenzerini, M.: On the interaction between ISA and cardinality constraints. In: Proc. of the 10th IEEE Int. Conf. on Data Engineering (ICDE’94), pp. 204–213. IEEE Computer Society Press, Los Alamitos (1994)Google Scholar
- 12.Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford Logic Guides 35 (1997)Google Scholar
- 14.ElMasri, R.A., Navathe, S.B.: Fundamentals of Database Systems, 5th edn. Addison Wesley Publ.Co. (2007)Google Scholar