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

    4 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 publicationCEUR Workshop Proceedings
    PublisherCEUR-WS
    Pages217-228
    Number of pages12
    Volume1466
    ISBN (Print)9782954494807
    Publication statusPublished - 2015
    Event12th International Conference on Concept Lattices and Their Applications, CLA 2015 - Clermont-Ferrand, France
    Duration: Oct 13 2015Oct 16 2015

    Other

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

    Fingerprint

    Formal concept analysis
    Artificial intelligence
    Redundancy

    ASJC Scopus subject areas

    • Computer Science(all)

    Cite this

    Rodríguez-Lorenzo, E., Adaricheva, K., Cordero, P., Enciso, M., & Mora, A. (2015). From an implicational system to its corresponding D-basis. In CEUR Workshop Proceedings (Vol. 1466, pp. 217-228). CEUR-WS.

    From an implicational system to its corresponding D-basis. / Rodríguez-Lorenzo, Estrella; Adaricheva, Kira; Cordero, Pablo; Enciso, Manuel; Mora, Angel.

    CEUR Workshop Proceedings. Vol. 1466 CEUR-WS, 2015. p. 217-228.

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

    Rodríguez-Lorenzo, E, Adaricheva, K, Cordero, P, Enciso, M & Mora, A 2015, From an implicational system to its corresponding D-basis. in CEUR Workshop Proceedings. vol. 1466, CEUR-WS, pp. 217-228, 12th International Conference on Concept Lattices and Their Applications, CLA 2015, Clermont-Ferrand, France, 10/13/15.
    Rodríguez-Lorenzo E, Adaricheva K, Cordero P, Enciso M, Mora A. From an implicational system to its corresponding D-basis. In CEUR Workshop Proceedings. Vol. 1466. CEUR-WS. 2015. p. 217-228
    Rodríguez-Lorenzo, Estrella ; Adaricheva, Kira ; Cordero, Pablo ; Enciso, Manuel ; Mora, Angel. / From an implicational system to its corresponding D-basis. CEUR Workshop Proceedings. Vol. 1466 CEUR-WS, 2015. pp. 217-228
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