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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Logical Analysis of Concept Lattices by Factorization
verfasst von : Eduard Bartl, Michal Krupka
Erschienen in: Formal Concept Analysis
Verlag: Springer Berlin Heidelberg
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Reducing the size of concept lattices is a well-known problem in Formal Concept Analysis. A particular instance of this problem is the size reduction of concept lattices using factorization by complete tolerances. We show that all complete tolerances on a complete lattice (i.e., all possible ways of factorizing the lattice) with a naturally-defined operation of multiplication form a residuated lattice. This allows looking at the set of all complete tolerances as a scale of truth degrees using which we can evaluate formulas of predicate logic specifying the desired parameters of the factorization. We present illustrative example to clarify our approach.