Boolean Substructures in Formal Concept Analysis

被引：1

作者：

Koyda, Maren ^{[1
,2
]}

Stumme, Gerd ^{[1
,2
]}

机构：

[1] Univ Kassel, Knowledge & Data Engn Grp, Kassel, Germany

[2] Univ Kassel, Interdisciplinary Res Ctr Informat Syst Design, Kassel, Germany

来源：

FORMAL CONCEPT ANALYSIS, ICFCA 2021 | 2021年 / 12733卷

关键词：

Formal Concept Analysis; Contranominal scales; Boolean contexts; Boolean lattices; Sublattices; Subcontexts; Closed relations;

D O I：

10.1007/978-3-030-77867-5_3

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

It is known that a (concept) lattice contains an n-dimensional Boolean suborder if and only if the context contains an n-dimensional contra-nominal scale as subcontext. In this work, we investigate more closely the interplay between the Boolean subcontexts of a given finite context and the Boolean suborders of its concept lattice. To this end, we define mappings from the set of subcontexts of a context to the set of suborders of its concept lattice and vice versa and study their structural properties. In addition, we introduce closed-subcontexts as an extension of closed relations to investigate the set of all sublattices of a given lattice.

引用

页码：38 / 53

页数：16

共 15 条

[1]

Albano A., 2017, Polynomial growth of concept lattices, canonical bases and generators: extremal set theory in formal concept analysis

[2]

Albano A, 2017, arXiv

[3]

Albano A., 2015, Proceedings of CLA, P73

[4]

Dias S., 2010, P CLA SEV SPAIN 1921, V672, P80

[5] Formal Context Generation Using Dirichlet Distributions [J].

Felde, Maximilian ;

Hanika, Tom .

GRAPH-BASED REPRESENTATION AND REASONING (ICCS 2019), 2019, 11530 :57-71

[6]

Ganter B., 1999, Formal Concept Analysis. Mathematical Foundations, DOI DOI 10.1007/978-3-642-59830-2

[7]

Ganter B, 2008, LECT NOTES ARTIF INT, V4933, P217, DOI 10.1007/978-3-540-78137-0_16

[8] Relevant Attributes in Formal Contexts [J].

Hanika, Tom ;

Koyda, Maren ;

Stumme, Gerd .

GRAPH-BASED REPRESENTATION AND REASONING (ICCS 2019), 2019, 11530 :102-116

[9] Generating complete sublattices by methods of formal concept analysis [J].

Kauer, Martin ;

Krupka, Michal .

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 2017, 46 (05) :475-489

[10]

Kuznetsov S., 1990, Autom. Doc. Math. Linguist., V24

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