Systems of implications obtained using the Carve decomposition of a formal context

Year: 2025

Type: article

Abstract: The Carve algorithm uses a divide-and-conquer strategy to compute the concept lattice of a formal context. The decomposition phase of the Carve algorithm discovers hierarchical structure in an amenable formal context, which the synthesis phase then exploits to construct the concept lattice from those of the component sub-contexts. In this paper, the problem of computing a sound and complete set of attribute implications via a refinement of the Carve decomposition is studied. Indeed, a set of rules is devised to obtain a set of valid implications which is proved to be complete. The refined decomposition and these rules are implemented in the novel Carve+ algorithm, whose runtime compares favorably with direct computation of the Duquenne–Guigues base of implications via the NextClosure algorithm.

Source: Knowledge-Based Systems

DOI: 10.1016/j.knosys.2025.113475

Authors: Domingo López-Rodríguez, Manuel Ojeda-Hernández, Tim Pattison

Institutions: Universidad de Málaga, Umeå University, Defence Science and Technology Group

Language: English

Topic: Rough Sets and Fuzzy Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,430

Funders: Ministerio de Ciencia, Innovación y Universidades, Kempe Foundation, Ministerio de Ciencia e Innovación, Kempestiftelserna, University of the East, European Regional Development Fund, Agencia Estatal de Investigación, European Social Fund

OpenAlex ID: W4409590910