A theory of finite closure spaces based on implications
type: Item
instance of: scholarly article
title: A theory of finite closure spaces based on implications
zbMATH Open document ID: 0863.54002
author: Marcel Wild
published in: Advances in Mathematics
publication date: 1995-01-02T00:00:00Z
review text: The theory of functional dependencies in relational database schemes is a neat example of a miniaturized logic: Notions like syntax, semantics, inference are present and the Amstron axioms are a simple tool to explain such fundamental concepts as soundness and completeness. It comes therefore as a surprise to observe that the very same notion can be the starting point for a research program on the interface between combinatorics (matroid theory), group theory, geometry (lattices) and topology (closure operators). The author seems to be involved in a general abstract characterization of minimal (optimal) systems of functional dependencies. In relational database theory these minimal covers are well understood; finding them is hard (NP-complete problems in the neighborhood). However, since the resulting characterizations are not translated backwards into the language of the application areas the question remains whether the characterizations have any merit other than being mathematically proven results. The reviewer failed to understood the relevance of the various notions of closure involved in this study for the database applications. I abstain from commenting on their relevance for combinatorics and/or topology. I do consider it unlikely however that the author has succeeded in his quest to rebut the prevalent opinion that ``no interesting space theory can be developed on the general concept of a closure space''.
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 68P15
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 51E99
zbMATH DE Number: 706489
zbMATH Keywords: implication bases
zbMATH Keywords: functional dependence
zbMATH Keywords: matroids
zbMATH Keywords: circuits
zbMATH Keywords: optimality
reviewed by: Peter van Emde Boas
MaRDI profile type: Publication
full work available at URL: aima.1994.1069
OpenAlex ID: W2072284346
DOI: 10.1006/AIMA.1994.1069
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description: scientific article; zbMATH DE number 706489