Simplifying Implications with Positive and Negative Attributes: A Logic-Based Approach

 

Abstract

Concepts and implications are two facets of the knowledge contained within a binary relation between objects and attributes. Simplification logic (SL) has proved to be valuable for the study of attribute implications in a concept lattice, a topic of interest in the more general framework of formal concept analysis (FCA). Specifically, SL has become the kernel of automated methods to remove redundancy or obtain different types of bases of implications. Although originally FCA used only the positive information contained in the dataset, negative information (explicitly stating that an attribute does not hold) has been proposed by several authors, but without an adequate set of equivalence-preserving rules for simplification. In this work, we propose a mixed simplification logic and a method to automatically remove redundancy in implications, which will serve as a foundational standpoint for the automated reasoning methods for this extended framework.

Funding

Projects funding this work

Citation

Please, cite this work as:

[Pér+22] F. Pérez-Gámez, D. López-Rodríguez, P. Cordero, et al. “Simplifying Implications with Positive and Negative Attributes: A Logic-Based Approach”. In: Mathematics 10.4 (2022). ISSN: 2227-7390. DOI: 10.3390/math10040607. URL: https://www.mdpi.com/2227-7390/10/4/607.

BibTeX

@Article{math10040607,
    AUTHOR = {Pérez-Gámez, Francisco and López-Rodríguez, Domingo and Cordero, Pablo and Mora, Ángel and Ojeda-Aciego, Manuel},
    TITLE = {Simplifying Implications with Positive and Negative Attributes: A Logic-Based Approach},
    JOURNAL = {Mathematics},
    VOLUME = {10},
    YEAR = {2022},
    NUMBER = {4},
    ARTICLE-NUMBER = {607},
    URL = {https://www.mdpi.com/2227-7390/10/4/607},
    ISSN = {2227-7390},
    ABSTRACT = {Concepts and implications are two facets of the knowledge contained within a binary relation between objects and attributes. Simplification logic (SL) has proved to be valuable for the study of attribute implications in a concept lattice, a topic of interest in the more general framework of formal concept analysis (FCA). Specifically, SL has become the kernel of automated methods to remove redundancy or obtain different types of bases of implications. Although originally FCA used only the positive information contained in the dataset, negative information (explicitly stating that an attribute does not hold) has been proposed by several authors, but without an adequate set of equivalence-preserving rules for simplification. In this work, we propose a mixed simplification logic and a method to automatically remove redundancy in implications, which will serve as a foundational standpoint for the automated reasoning methods for this extended framework.},
    DOI = {10.3390/math10040607}
}

Bibliometric data

The following data has been extracted from resources such as OpenAlex, Dimensions, PlumX or Altmetric.

6

CITATIONS

6 Total citations

3 Recent citations

n/a Field Citation Ratio

n/a Relative Citation Ratio

• Citations
• CrossRef - Citation Indexes: 6
• Scopus - Citation Indexes: 8

• Captures
• Mendeley - Readers: 2

-

see details

See more details

Posted by 2 X users

2 readers on Mendeley

Cites

The following graph plots the number of cites received by this work from its publication, on a yearly basis.

Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] Ľ. Antoni, P. Eliaš, J. Guniš, et al. “Bimorphisms and attribute implications in heterogeneous formal contexts”. In: International Journal of Approximate Reasoning 172 (Sep. 2024), p. 109245. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2024.109245. URL: http://dx.doi.org/10.1016/j.ijar.2024.109245.

[2] F. Chacón-Gómez, M. E. Cornejo, and J. Medina. “Towards Confirmation Measures to Mixed Attribute Implications”. In: Graph-Based Representation and Reasoning. Springer Nature Switzerland, 2023, p. 193–196. ISBN: 9783031409608. DOI: 10.1007/978-3-031-40960-8_16. URL: http://dx.doi.org/10.1007/978-3-031-40960-8_16.

[3] F. Chacón-Gómez, M. E. Cornejo, J. Medina, et al. “Rough set decision algorithms for modeling with uncertainty”. In: Journal of Computational and Applied Mathematics 437 (Feb. 2024), p. 115413. ISSN: 0377-0427. DOI: 10.1016/j.cam.2023.115413. URL: http://dx.doi.org/10.1016/j.cam.2023.115413.

[4] J. Liu, J. Mi, and D. Niu. “A novel method for generating a canonical basis for decision implications based on object-induced three-way operators”. In: Knowledge-Based Systems 283 (Jan. 2024), p. 111161. ISSN: 0950-7051. DOI: 10.1016/j.knosys.2023.111161. URL: http://dx.doi.org/10.1016/j.knosys.2023.111161.

[5] D. López-Rodríguez, M. Ojeda-Hernández, and C. Bejines. “New Simplification Rules for Databases with Positive and Negative Attributes”. In: Mathematics 13.2 (Jan. 2025), p. 309. ISSN: 2227-7390. DOI: 10.3390/math13020309. URL: http://dx.doi.org/10.3390/math13020309.

[6] P. Sokol, Ľ. Antoni, O. Krídlo, et al. “Formal concept analysis approach to understand digital evidence relationships”. In: International Journal of Approximate Reasoning 159 (Aug. 2023), p. 108940. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2023.108940. URL: http://dx.doi.org/10.1016/j.ijar.2023.108940.

[7] J. Xu, C. Wu, J. Xu, et al. “Stream Convolution for Attribute Reduction of Concept Lattices”. In: Mathematics 11.17 (Aug. 2023), p. 3739. ISSN: 2227-7390. DOI: 10.3390/math11173739. URL: http://dx.doi.org/10.3390/math11173739.