Geodesic
Classification systems and their lattice
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2, pp. 167-181

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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent and Cls(L) is a partition lattice.
Keywords: concept lattice, CJ-generated complete lattice, atomistic complete lattice, (independent) classification system, classification lattice, box lattice 
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Radeleczki, Sándor. Classification systems and their lattice. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2, pp. 167-181. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_2_a6/