From an implicational system to its corresponding D-basis

Estrella Rodríguez-Lorenzo, Kira Adaricheva, Pablo Cordero, Manuel Enciso, Angel Mora

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

Closure system is a fundamental concept appearing in several areas such as databases, formal concept analysis, artificial intelligence, etc. It is well-known that there exists a connection between a closure operator on a set and the lattice of its closed sets. Furthermore, the closure system can be replaced by a set of implications but this set has usually a lot of redundancy inducing non desired properties. In the literature, there is a common interest in the search of the minimality of a set of implications because of the importance of bases. The well-known Duquenne-Guigues basis satisfies this minimality condition. However, several authors emphasize the relevance of the optimality in order to reduce the size of implications in the basis. In addition to this, some bases have been defined to improve the computation of closures relying on the directness property. The efficiency of computation with the direct basis is achieved due to the fact that the closure is computed in one traversal. In this work, we focus on the D-basis, which is ordered-direct. An open problem is to obtain it from an arbitrary implicational system, so it is our aim in this paper. We introduce a method to compute the D-basis by means of minimal generators calculated using the Simplification Logic for implications.

Original languageEnglish
Title of host publication12th International Conference on Concept Lattices and Their Applications, CLA 2015
EditorsSadok Ben Yahia, Jan Konecny
PublisherCEUR-WS
Pages217-228
Number of pages12
ISBN (Electronic)9782954494807
Publication statusPublished - Jan 1 2015
Event12th International Conference on Concept Lattices and Their Applications, CLA 2015 - Clermont-Ferrand, France
Duration: Oct 13 2015Oct 16 2015

Publication series

NameCEUR Workshop Proceedings
Volume1466
ISSN (Print)1613-0073

Other

Other12th International Conference on Concept Lattices and Their Applications, CLA 2015
CountryFrance
CityClermont-Ferrand
Period10/13/1510/16/15

ASJC Scopus subject areas

  • Computer Science(all)

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