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

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 c...
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Autor*in:	Francisco Pérez-Gámez [verfasserIn] Domingo López-Rodríguez [verfasserIn] Pablo Cordero [verfasserIn] Ángel Mora [verfasserIn] Manuel Ojeda-Aciego [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	formal concept analysis implicational systems negative attributes

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 10(2022), 4, p 607
Übergeordnetes Werk:	volume:10 ; year:2022 ; number:4, p 607

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math10040607

Katalog-ID:	DOAJ069454035

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author	Francisco Pérez-Gámez
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title_auth	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.
abstractGer	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.
abstract_unstemmed	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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