Year: 2018
Type: preprint
Abstract: The notions of formal contexts and concept lattices, although introduced by Wille only ten years ago, already have proven to be of great utility in various applications such as data analysis and knowledge representation. In this paper we give arguments that Wille's original notion of formal context, although quite appealing in its simplicity, now should be replaced by a more semantic notion. This new notion of formal context entails a modified approach to concept construction. We base our arguments for these new versions of formal context and concept construction upon Wille's philosophical attitude with reference to the intensional aspect of concepts. We give a brief development of the relational theory of formal contexts and concept construction, demonstrating the equivalence of "concept-lattice construction" of Wille with the well-known "completion by cuts" of MacNeille. Generalization and abstraction of these formal contexts offers a powerful approach to knowledge representation.
Source: arXiv (Cornell University)
Author: Kent, Robert E.
Institution: University of Arkansas at Little Rock
Language: English
Topic: Rough Sets and Fuzzy Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2896145341