Abstract
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.
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Bartl, E., Krupka, M. (2012). Logical Analysis of Concept Lattices by Factorization. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds) Formal Concept Analysis. ICFCA 2012. Lecture Notes in Computer Science(), vol 7278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29892-9_8
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DOI: https://doi.org/10.1007/978-3-642-29892-9_8
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