The generalized doubling construction and formal concept analysis
type: Item
instance of: scholarly article
title: The generalized doubling construction and formal concept analysis
zbMATH Open document ID: 0829.06007
DOI: 10.1007/BF01235175
author: Winfried Geyer
published in: Algebra Universalis
publication date: 1996-01-21T00:00:00Z
review text: A. Day introduced the interval doubling construction to prove Whitman's structure theorem for free lattices. Here the doubling of a convex set \(C\) in a lattice \(L\) is described by an equivalent context operation in formal concept analysis, which assigns to the standard context \(\mathbb{K} (L)\) a new context \(\mathbb{K} (L) [C]\). Now, \(L(C)\), the lattice given by the doubling of the convex set \(C\), is isomorphic to the concept lattice of this new context. If the doubling of intervals starts from the two- element lattice, then the lattices become semi-distributive.
reviewed by: Dietmar Schweigert
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B99
zbMATH DE Number: 695409
zbMATH Keywords: semi-distributive lattices
zbMATH Keywords: doubling of a convex set
zbMATH Keywords: context operation
zbMATH Keywords: formal concept analysis
zbMATH Keywords: concept lattice
zbMATH Keywords: doubling of intervals
MaRDI profile type: Publication
cites work: A Simple Solution to the Word Problem for Lattices
cites work: Splitting lattices generate all lattices
cites work: Characterizations of Finite Lattices that are Bounded-Homomqrphic Images or Sublattices of Free Lattices
cites work: Congruence normality: The characterization of the doubling class of convex sets
cites work: Doubling convex sets in lattices and a generalized semidistributivity condition
cites work: Generalizing semidistributivity
cites work: On Tamari lattices
cites work: Q4165427
cites work: Almost distributive lattice varieties
cites work: Equational Bases and Nonmodular Lattice Varieties
cites work: Finite Sublattices of a Free Lattice
cites work: Q3952147
cites work: Subdirect decomposition of concept lattices
description: scientific article; zbMATH DE number 695409