Simplification logic for the management of unknown information

 

Abstract

This paper aims to contribute to the extension of classical Formal Concept Analysis (FCA), allowing the management of unknown information. In a preliminary paper, we define a new kind of attribute implications to represent the knowledge from the information currently available. The whole FCA framework has to be appropriately extended to manage unknown information. This paper introduces a new logic for reasoning with this kind of implications, which belongs to the family of logics with an underlying Simplification paradigm. Specifically, we introduce a new algebra, named weak dual Heyting Algebra, that allows us to extend the Simplification logic for these new implications. To provide a solid framework, we also prove its soundness and completeness and show the advantages of the Simplification paradigm. Finally, to allow further use of this extension of FCA in applications, an algorithm for automated reasoning, which is directly built from logic, is defined.

Citation

Please, cite this work as:

[Pér+23] F. Pérez-Gámez, P. Cordero, M. Enciso, et al. “Simplification logic for the management of unknown information”. In: Information Sciences 634 (2023), pp. 505-519. ISSN: 0020-0255. DOI: https://doi.org/10.1016/j.ins.2023.03.015. URL: https://www.sciencedirect.com/science/article/pii/S0020025523003110.

BibTeX

@article{PEREZGAMEZ2023505,
    title = {Simplification logic for the management of unknown information},
    journal = {Information Sciences},
    volume = {634},
    pages = {505-519},
    year = {2023},
    issn = {0020-0255},
    doi = {https://doi.org/10.1016/j.ins.2023.03.015},
    url = {https://www.sciencedirect.com/science/article/pii/S0020025523003110},
    author = {Francisco Pérez-Gámez and Pablo Cordero and Manuel Enciso and Ángel Mora},
    keywords = {Implications, Unknown information, Formal concept analysis, Simplification logic, Automated reasoning},
    abstract = {This paper aims to contribute to the extension of classical Formal Concept Analysis (FCA), allowing the management of unknown information. In a preliminary paper, we define a new kind of attribute implications to represent the knowledge from the information currently available. The whole FCA framework has to be appropriately extended to manage unknown information. This paper introduces a new logic for reasoning with this kind of implications, which belongs to the family of logics with an underlying Simplification paradigm. Specifically, we introduce a new algebra, named weak dual Heyting Algebra, that allows us to extend the Simplification logic for these new implications. To provide a solid framework, we also prove its soundness and completeness and show the advantages of the Simplification paradigm. Finally, to allow further use of this extension of FCA in applications, an algorithm for automated reasoning, which is directly built from logic, is defined.}
}

Bibliometric data

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8

CITATIONS

8 Total citations

8 Recent citations

5.31 Field Citation Ratio

n/a Relative Citation Ratio

• Citations
• Scopus - Citation Indexes: 8

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• Mendeley - Readers: 4

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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] R. G. Aragón, J. Medina, and S. Molina-Ruiz. “The Notion of Bond in the Multi-adjoint Concept Lattice Framework”. In: Advances in Artificial Intelligence. Springer Nature Switzerland, 2024, p. 243–253. ISBN: 9783031627996. DOI: 10.1007/978-3-031-62799-6_25. URL: http://dx.doi.org/10.1007/978-3-031-62799-6_25.

[2] P. Cordero, M. Enciso, Á. Mora, et al. “Attribute implications with unknown information based on weak Heyting algebras”. In: Fuzzy Sets and Systems 490 (Aug. 2024), p. 109026. ISSN: 0165-0114. DOI: 10.1016/j.fss.2024.109026. URL: http://dx.doi.org/10.1016/j.fss.2024.109026.

[3] M. E. Cornejo, J. Medina, and F. J. Ocaña. “Attribute implications in multi-adjoint concept lattices with hedges”. In: Fuzzy Sets and Systems 479 (Mar. 2024), p. 108854. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.108854. URL: http://dx.doi.org/10.1016/j.fss.2023.108854.

[4] D. Dubois, J. Medina, and H. Prade. “Extracting attribute implications from a formal context: Unifying the basic approaches”. In: Information Sciences 689 (Jan. 2025), p. 121419. ISSN: 0020-0255. DOI: 10.1016/j.ins.2024.121419. URL: http://dx.doi.org/10.1016/j.ins.2024.121419.

[5] D. López-Rodríguez, M. Ojeda-Hernández, and T. Pattison. “Systems of implications obtained using the Carve decomposition of a formal context”. In: Knowledge-Based Systems (Apr. 2025), p. 113475. ISSN: 0950-7051. DOI: 10.1016/j.knosys.2025.113475. URL: http://dx.doi.org/10.1016/j.knosys.2025.113475.

[6] F. Pérez-Gámez and C. Bejines. “An exploration of weak Heyting algebras: Characterization and properties”. In: International Journal of Approximate Reasoning 179 (Apr. 2025), p. 109365. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2025.109365. URL: http://dx.doi.org/10.1016/j.ijar.2025.109365.

[7] F. J. Talavera, C. Bejines, S. Ardanza-Trevijano, et al. “Aggregation of fuzzy graphs”. In: International Journal of Approximate Reasoning 172 (Sep. 2024), p. 109243. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2024.109243. URL: http://dx.doi.org/10.1016/j.ijar.2024.109243.