Subdirect decomposition of concept lattices

descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book , Conference object 01 Dec 1983 English Publisher:Springer Science and Business Media LLCJournal:Algebra Universalis, volume 17, pages 275-287 (issn: 0002-5240, eissn: 1420-8911,

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Authors: Rudolf Wille;

doi: 10.1007/bf01194537 , 10.1007/978-3-319-07248-7_20

Subdirect decomposition of concept lattices

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Abstract

This paper is a continuation of a previous paper of the author where the basic theorem for ''concept lattices'' has been given [Ordered sets, Proc. NATO Adv. Study Inst., Banff/Can. 1981, 445-470 (1982; Zbl 0491.06008)]. A concept lattice can be regarded as a complete meet-sublattice of the power set lattice of ''objects'' determined by the Galois connection given by the ''attributes'' in the obvious way. The purpose of the paper is for some special kind of context to determine the ''scaffolding'' the concept lattice which is a partial join-semilattice. From this result one can determine the concept lattice using an earlier result of the author.

Related Organizations

Darmstadt University of Applied Sciences
Germany

Keywords

complete meet-sublattice, partial join-semilattice, Galois correspondences, closure operators (in relation to ordered sets), Structure theory of lattices, Representation theory of lattices, concept lattice, Complete lattices, completions, power set lattice, Galois connection

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