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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| Published in: | Knowledge-based systems Vol. 318; p. 113475 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
07.06.2025
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| ISSN: | 0950-7051, 1872-7409 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 113475 |
| Author | Ojeda-Hernández, Manuel López-Rodríguez, Domingo Pattison, Tim |
| Author_xml | – sequence: 1 givenname: Domingo surname: López-Rodríguez fullname: López-Rodríguez, Domingo email: dominlopez@uma.es organization: Departamento de Matemática Aplicada, Universidad de Málaga, Andalucía Tech, Málaga, 29071, Spain – sequence: 2 givenname: Manuel orcidid: 0000-0003-4785-6802 surname: Ojeda-Hernández fullname: Ojeda-Hernández, Manuel email: manueloh@cs.umu.se organization: Department of Computing Science, Umeå University, Sweden – sequence: 3 givenname: Tim surname: Pattison fullname: Pattison, Tim email: tim.pattison@ieee.org organization: Defence Science and Technology Group, West Avenue, Edinburgh, SA 5111, Australia |
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| Keywords | Formal concept analysis 06A15 Divide-and-conquer algorithms 03B70 Attribute implications 06-04 Knowledge representation Implicational systems |
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| Title | Systems of implications obtained using the Carve decomposition of a formal context |
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