On The Satisfiability of Dependency Constraints in Entity-Relationship Schemata.

Maurizio Lenzerini, Paolo Nobili: On The Satisfiability of Dependency Constraints in Entity-Relationship Schemata. VLDB 1987: 147-154
  author    = {Maurizio Lenzerini and
               Paolo Nobili},
  editor    = {Peter M. Stocker and
               William Kent and
               Peter Hammersley},
  title     = {On The Satisfiability of Dependency Constraints in Entity-Relationship
  booktitle = {VLDB'87, Proceedings of 13th International Conference on Very
               Large Data Bases, September 1-4, 1987, Brighton, England},
  publisher = {Morgan Kaufmann},
  year      = {1987},
  isbn      = {0-934613-46-X},
  pages     = {147-154},
  ee        = {db/conf/vldb/LenzeriniN87.html},
  crossref  = {DBLP:conf/vldb/87},
  bibsource = {DBLP,}


The problem of satisfiability of a specific class of integrity constraints in data bases, namely the dependency constraints, is analysed. An Entity-Relationship model is used for expressing data schemata. In this model suitable types of dependency constraints, called cardinality ratio constraints, allow one to impose restrictions on the mappings between entities and relationships. We show that, as far as such a class of constraints is concerned, the usual notion of satisfiability is not sufficiently meaningful. For this reason we introduce the notion of strong satisfiability, ensuring that no entity or relationship is compelled to be empty in all of the legal instances of the schema. We propose to model the cardinality ratio constraints of a schema by means of a suitable linear inequality system and we show that a schema is strongly satisfiable if and only if there exist solutions for the associated system. Furthermore, we describe a method for discovering which are the sets of constraints that prevent a schema from being strongly satisfiable.

Copyright © 1987 by the VLDB Endowment. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by the permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment.

Online Paper

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Printed Edition

Peter M. Stocker, William Kent, Peter Hammersley (Eds.): VLDB'87, Proceedings of 13th International Conference on Very Large Data Bases, September 1-4, 1987, Brighton, England. Morgan Kaufmann 1987, ISBN 0-934613-46-X
Contents BibTeX


Antonio Albano, Luca Cardelli, Renzo Orsini: Galileo: A Strongly-Typed, Interactive Conceptual Language. ACM Trans. Database Syst. 10(2): 230-260(1985) BibTeX
Peter P. Chen: The Entity-Relationship Model - Toward a Unified View of Data. ACM Trans. Database Syst. 1(1): 9-36(1976) BibTeX
Michael Hammer, Dennis McLeod: Database Description with SDM: A Semantic Database Model. ACM Trans. Database Syst. 6(3): 351-386(1981) BibTeX
Maurizio Lenzerini: SERM: Semantic Entity-Relationship Model. ER 1985: 270-278 BibTeX
Christos H. Papadimitriou, Kenneth Steiglitz: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall 1982, ISBN 0-13-152462-3
Jeffrey D. Ullman: Principles of Database Systems, 2nd Edition. Computer Science Press 1982, ISBN 0-914894-36-6

Referenced by

  1. Giuseppe Di Battista, Maurizio Lenzerini: A Deductive Method for Entity-Relationship Modeling. VLDB 1989: 13-21
  2. Giuseppe Di Battista, Maurizio Lenzerini: Object Modeling Based on Logic. ER 1988: 207-225
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