If one wishes to examine parts of a rather complex concept system, it seems reasonable to exclude some objects and/or attributes from the examination. We shall describe the effects of this procedure on the concept lattice. The concept lattice of a subcontext always has an order-embedding into that of the original context. Much more information can be obtained when dealing with compatible subcontexts, which will be introduced later in this section. It is easy to identify these particular subcontexts by means of the arrow relations. Thus we obtain a factor lattice of the original concept lattice. The interrelations between factor lattices, congruence relations and such subcontexts will be described in the second section.
KeywordsSmall Element Complete Lattice Homomorphic Image Concept Lattice Congruence Relation
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