Technical Reports (CIS)

Document Type

Technical Report

Date of this Version

November 1990

Comments

University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-90-85.

Abstract

In this paper we study direct product decompositions of closure operations and lattices of closed sets. We characterize direct product decompositions of lattices of closed sets in terms of closure operations, and find those decompositions of lattices which correspond to the decompositions of closures. If a closure on a finite set is represented by its implication base (i.e. a binary relation on a powerset), we construct a polynomial algorithm to find its direct product decompositions. The main characterization theorem is also applied to define direct product decompositions of relational database schemes and to find out what properties of relational databases and schemes are preserved under decompositions.

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Date Posted: 14 August 2007