Galois Connections and Data Analysis

Issue title: Concurrency Specification and Programming (CS&P 2003)

Article type: Research Article

Authors: Wolski, Marcin

Affiliations: Department of Logic and Methodology of Science, Maria Curie-Skłodowska University, Lublin, Poland

Abstract: We investigate Galois connections and their relations to the major theories of (qualitative) data analysis: Rough Set Theory (RST), Formal Concept Analysis (FCA) and John Stuart Mill Reasoning (JSM-Reasoning). Polarities, a type of contravariant Galois connections, and their relationships with data analysis has been already well-known. This paper shows how axialities, a type of covariant Galois connections, are related to problems adressed by data analysis and prove that they give rise to a number of interesting lattices.

Keywords: galois connection, polarity lattice, axiality, concept, rough set, lattice

Journal: Fundamenta Informaticae, vol. 60, no. 1-4, pp. 401-415, 2004