Formation of the D-basis from implicational systems using Simplification logic
Abstract
Sets of implications defining closure systems are used as a standard way to represent knowledge, and the search of implicational systems satisfying some criteria constitutes one of the most active topics in the study of closure systems and their applications. Here, we focus on the generation of the D-basis, known to be an ordered direct basis, allowing a very efficient attribute closure computation. We operate with the aggregated D-basis and provide an algorithm to get it from an arbitrary implicational set. The method has been designed on the interrelation between minimal covers and minimal generators, and it is inspired by the inference system of the Simplification Logic. Moreover, we develop an experiment to show the better performance of the new method compared to the earlier version of the algorithm.
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Please, cite this work as:
[Rod+17] E. Rodr', K. V. Adaricheva, P. Cordero, et al. “Formation of the D-basis from implicational systems using Simplification logic”. In: Int. J. Gen. Syst. 46.5 (2017), pp. 547-568. DOI: 10.1080/03081079.2017.1349632. URL: https://doi.org/10.1080/03081079.2017.1349632.
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Papers citing this work
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[1] K. Adaricheva and T. Ninesling. “Direct and Binary Direct Bases for One-Set Updates of a Closure System”. In: Formal Concept Analysis. Springer International Publishing, 2019, p. 55–72. ISBN: 9783030214623. DOI: 10.1007/978-3-030-21462-3_5. URL: http://dx.doi.org/10.1007/978-3-030-21462-3_5.
[2] R. G. Aragón, M. Eugenia Cornejo, J. Medina, et al. “A Formal Method for Driver Identification”. In: Computational Intelligence and Mathematics for Tackling Complex Problems 4. Springer International Publishing, Sep. 2022, p. 153–159. ISBN: 9783031077074. DOI: 10.1007/978-3-031-07707-4_19. URL: http://dx.doi.org/10.1007/978-3-031-07707-4_19.
[3] P. Cordero, M. Enciso, A. Mora, et al. “Interactive Search by Using Minimal Generators”. In: Computational Intelligence and Mathematics for Tackling Complex Problems 2. Springer International Publishing, 2022, p. 147–153. ISBN: 9783030888176. DOI: 10.1007/978-3-030-88817-6_17. URL: http://dx.doi.org/10.1007/978-3-030-88817-6_17.
[4] P. Cordero, M. Enciso, Á. Mora, et al. “A Formal Concept Analysis Approach to Cooperative Conversational Recommendation”. In: International Journal of Computational Intelligence Systems 13.1 (2020), p. 1243. ISSN: 1875-6883. DOI: 10.2991/ijcis.d.200806.001. URL: http://dx.doi.org/10.2991/ijcis.d.200806.001.
[5] D. López-Rodríguez, E. Muñoz-Velasco, and M. Ojeda-Aciego. “Formal Methods in FCA and Big Data”. In: Complex Data Analytics with Formal Concept Analysis. Springer International Publishing, Dec. 2021, p. 201–224. ISBN: 9783030932787. DOI: 10.1007/978-3-030-93278-7_9. URL: http://dx.doi.org/10.1007/978-3-030-93278-7_9.
[6] T. Pattison, M. Enciso, Á. Mora, et al. “Scalable Visual Analytics in FCA”. In: Complex Data Analytics with Formal Concept Analysis. Springer International Publishing, Dec. 2021, p. 167–200. ISBN: 9783030932787. DOI: 10.1007/978-3-030-93278-7_8. URL: http://dx.doi.org/10.1007/978-3-030-93278-7_8.