A tableaux-like method to infer all minimal keys
Abstract
The problem of enumerating a kind of minimal generator from a set of if–then rules is addressed. The if–then rules are widely used in several areas and always are associated with a closure operator in a set. So, they are used in databases as functional dependencies and in formal concept analysis as implications. In this article, the minimal generators to be enumerated are those that generate the full set, also called minimal keys. There are several ad hoc approaches corresponding to particular instances of the key finding problem, but our objective is to provide a general approach directly based on logic. More specifically we use a tableaux-like method to find all minimal keys. We select the tableaux-like approach because it allows to design new methods by incorporating new inference rules and new strategies. In this work, we present a new method which is more efficient than previous tableaux-like methods.
Citation
Please, cite this work as:
[Cor+14] P. Cordero, M. Enciso, Á. Mora, et al. “A tableaux-like method to infer all minimal keys”. In: Log. J. IGPL 22.6 (2014), pp. 1019-1044. DOI: 10.1093/JIGPAL/JZU025. URL: https://doi.org/10.1093/jigpal/jzu025.
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Papers citing this work
The following is a non-exhaustive list of papers that cite this work:
[1] F. Benito-Picazo, P. Cordero, M. Enciso, et al. “Reducing the search space by closure and simplification paradigms: A parallel key finding method”. In: The Journal of Supercomputing 73.1 (Jan. 2016), p. 75–87. ISSN: 1573-0484. DOI: 10.1007/s11227-016-1622-1. URL: http://dx.doi.org/10.1007/s11227-016-1622-1.
[2] F. Benito‐Picazo, M. Enciso, C. Rossi, et al. “Enhancing the conversational process by using a logical closure operator in phenotypes implications”. In: Mathematical Methods in the Applied Sciences 41.3 (Feb. 2017), p. 1089–1100. ISSN: 1099-1476. DOI: 10.1002/mma.4338. URL: http://dx.doi.org/10.1002/mma.4338.
[3] 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.
[4] P. Cordero, M. Enciso, A. Mora, et al. “Parameterized simplification logic I: reasoning with implications and classes of closure operators”. In: International Journal of General Systems 49.7 (Oct. 2020), p. 724–746. ISSN: 1563-5104. DOI: 10.1080/03081079.2020.1831484. URL: http://dx.doi.org/10.1080/03081079.2020.1831484.
[5] M. Demba. “KeyFinder: An Efficient Minimal Keys Finding Algorithm For Relational Databases”. In: Inteligencia Artificial 24.68 (Sep. 2021), p. 37–52. ISSN: 1137-3601. DOI: 10.4114/intartif.vol24iss68pp37-52. URL: http://dx.doi.org/10.4114/intartif.vol24iss68pp37-52.
[6] N. Leutwyler, M. Lezoche, C. Franciosi, et al. “Methods for concept analysis and multi-relational data mining: a systematic literature review”. In: Knowledge and Information Systems 66.9 (May. 2024), p. 5113–5150. ISSN: 0219-3116. DOI: 10.1007/s10115-024-02139-x. URL: http://dx.doi.org/10.1007/s10115-024-02139-x.
[7] M. Ojeda-Hernández, I. P. Cabrera, and P. Cordero. “Quasi-closed elements in fuzzy posets”. In: Journal of Computational and Applied Mathematics 404 (Apr. 2022), p. 113390. ISSN: 0377-0427. DOI: 10.1016/j.cam.2021.113390. URL: http://dx.doi.org/10.1016/j.cam.2021.113390.
[8] E. Rodríguez-Lorenzo, P. Cordero, M. Enciso, et al. “Canonical dichotomous direct bases”. In: Information Sciences 376 (Jan. 2017), p. 39–53. ISSN: 0020-0255. DOI: 10.1016/j.ins.2016.10.004. URL: http://dx.doi.org/10.1016/j.ins.2016.10.004.