Partition Semantics for Relations.

Stavros S. Cosmadakis, Paris C. Kanellakis, Nicolas Spyratos: Partition Semantics for Relations. PODS 1985: 261-275
  author    = {Stavros S. Cosmadakis and
               Paris C. Kanellakis and
               Nicolas Spyratos},
  title     = {Partition Semantics for Relations},
  booktitle = {Proceedings of the Fourth ACM SIGACT-SIGMOD Symposium on Principles
               of Database Systems, March 25-27, 1985, Portland, Oregon},
  publisher = {ACM},
  year      = {1985},
  isbn      = {0-89791-153-9},
  pages     = {261-275},
  ee        = {, db/conf/pods/CosmadakisKS85.html},
  crossref  = {DBLP:conf/pods/85},
  bibsource = {DBLP,}


Set-theoretic partitions were first used in [15] to provide models for relation schemes, relations and dependencies. This new point of view of the relational model demonstrates that there is a natural extension of functional dependencies (FD's), which is based on the duality between product and sum of partitions. We show that these partition dependencies (PD's) have the power to express both functional determination and transitive closure of undirected graphs. The inference problem of PD's is shown to be the uniform word problem in a lattice. We provide a polynomial time algorithm for this natural generalization of the FD inference problem. We show how partition semantics justify a number of variants of the weak instance assumption and investigate the expressive power of PD's. We also provide a polynomial time test for consistency of a set of relations with a set of PD's.

Copyright © 1985 by the ACM, Inc., used by permission. Permission to make digital or hard copies is granted provided that copies are not made or distributed for profit or direct commercial advantage, and that copies show this notice on the first page or initial screen of a display along with the full citation.

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Proceedings of the Fourth ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, March 25-27, 1985, Portland, Oregon. ACM 1985, ISBN 0-89791-153-9
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Journal Version

Stavros S. Cosmadakis, Paris C. Kanellakis, Nicolas Spyratos: Partition Semantics for Relations. J. Comput. Syst. Sci. 33(2): 203-233(1986) BibTeX


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Referenced by

  1. Dominique Laurent, Nicolas Spyratos: A Partition Model Approach to Updating Universal Scheme Interfaces. IEEE Trans. Knowl. Data Eng. 6(2): 316-330(1994)
  2. Chris Tuijn, Marc Gyssens: Views and Decompositions of Databases from a Categorical Perspective. ICDT 1992: 99-112
  3. Christophe Lécluse, Nicolas Spyratos: Implementing Queries and Updates on Universal Scheme Interfaces. VLDB 1988: 62-75
  4. Dominique Laurent, Nicolas Spyratos: Partition Semantics for Incomplete Information in Relational Databases. SIGMOD Conference 1988: 66-73
  5. Nicolas Spyratos, Christophe Lécluse: Incorporating Functional Dependencies in Deductive Query Answering. ICDE 1987: 658-664
  6. Moshe Y. Vardi: On the Integrity of Databases with Incomplete Information. PODS 1986: 252-266
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