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

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 thos...

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Bibliographic Details
Published in:Knowledge-based systems Vol. 318; p. 113475
Main Authors: López-Rodríguez, Domingo, Ojeda-Hernández, Manuel, Pattison, Tim
Format: Journal Article
Language:English
Published: Elsevier B.V 07.06.2025
Subjects:
Attribute implications
Divide-and-conquer algorithms
Formal concept analysis
Implicational systems
Knowledge representation
Formal concept analysis
06A15
Divide-and-conquer algorithms
03B70
Attribute implications
06-04
Knowledge representation
Implicational systems
ISSN:0950-7051, 1872-7409
Online Access:Get full text
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Summary: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.
ISSN:0950-7051
1872-7409
DOI:10.1016/j.knosys.2025.113475