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

Francisco Pérez-Gámez, Domingo López-Rodríguez, Pablo Cordero, Ángel Mora and Manuel Ojeda-Aciego
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Francisco Pérez-Gámez: Departamento Matemática Aplicada, Universidad de Málaga, 29071 Málaga, Spain
Domingo López-Rodríguez: Departamento Matemática Aplicada, Universidad de Málaga, 29071 Málaga, Spain
Pablo Cordero: Departamento Matemática Aplicada, Universidad de Málaga, 29071 Málaga, Spain
Ángel Mora: Departamento Matemática Aplicada, Universidad de Málaga, 29071 Málaga, Spain
Manuel Ojeda-Aciego: Departamento Matemática Aplicada, Universidad de Málaga, 29071 Málaga, Spain

Mathematics, 2022, vol. 10, issue 4, 1-19

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.

Keywords: formal concept analysis; implicational systems; negative attributes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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