Subdirect decomposition of concept lattices

Abstract

In [1], G.Birkhoff exhibited the subdirect product of algebraic structures as a universal tool, which since has been extensively used in the study of algebraic theories. Although a subdirect product is not uniquely determined by its factors, there are useful construction methods based on subdirect products (cf. Wille [8], [9], [10]). The aim of this paper is to make these methods available for handling the "Determination Problem" of concept lattices as it is exposed in Wille [11]. In particular, a useful method for determining concept lattices via its scaffoldings will be developed under some finiteness condition. © 2014 Springer International Publishing.