Abstract
The most popular basis in Formal Concept Analysis is the Duquenne-Guigues basis, which ensure minimality in the number of dependencies and it is built with pseudo-intents, and some method to calculate these basis from an arbitrary set of implications have been introduced. We propose in this paper, an automated method to calculate a left-minimal direct basis from the set of all implications built between a closed set and its corresponding minimal generators. The new basis also has the minimal property demanded in the Duquenne-Guigues basis. It is minimal in the cardinal of the set of implications, and minimal in the size of the left-hand side of the implications.
Citation
Please, cite this work as:
[Cor+13] P. Cordero, M. Enciso, Á. Mora, et al. “Computing Left-Minimal Direct Basis of implications”. In: Proceedings of the Tenth International Conference on Concept Lattices and Their Applications, La Rochelle, France, October 15-18, 2013. Ed. by M. Ojeda-Aciego and J. Outrata. Vol. 1062. CEUR Workshop Proceedings. CEUR-WS.org, 2013, pp. 293-298. URL: https://ceur-ws.org/Vol-1062/paper_short4.pdf.
@InProceedings{Cordero2013,
author = {Pablo Cordero and Manuel Enciso and {’A}ngel Mora and Manuel Ojeda-Aciego},
booktitle = {Proceedings of the Tenth International Conference on Concept Lattices and Their Applications, La Rochelle, France, October 15-18, 2013},
title = {Computing Left-Minimal Direct Basis of implications},
year = {2013},
editor = {Manuel Ojeda-Aciego and Jan Outrata},
pages = {293–298},
publisher = {CEUR-WS.org},
series = {{CEUR} Workshop Proceedings},
volume = {1062},
abstract = {The most popular basis in Formal Concept Analysis is the Duquenne-Guigues basis, which ensure minimality in the number of dependencies and it is built with pseudo-intents, and some method to calculate these basis from an arbitrary set of implications have been introduced. We propose in this paper, an automated method to calculate a left-minimal direct basis from the set of all implications built between a closed set and its corresponding minimal generators. The new basis also has the minimal property demanded in the Duquenne-Guigues basis. It is minimal in the cardinal of the set of implications, and minimal in the size of the left-hand side of the implications.},
bibsource = {dblp computer science bibliography, https://dblp.org},
biburl = {https://dblp.org/rec/conf/cla/CorderoEMO13.bib},
timestamp = {Fri, 10 Mar 2023 16:22:10 +0100},
url = {https://ceur-ws.org/Vol-1062/paper_short4.pdf},
}