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.

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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}
}