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 
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/
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