Abstract
We study the “non-unit implications” of a formal context and investigate the closure system induced by these implications. It turns out that this closure system is the largest closure system on the same base set containing the given one as a complete sublattice. This was studied by other authors with special emphasis on semidistributivity and convex geometries. We present some of their results in FCA language.
The complete lattice refinements of a closure system form an interval within the lattice of all closure systems. We describe the reduced context for this interval.
For better compatibility with the literature, we dualize and consider implications between objects, not attributes.
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Ganter, B., Reppe, H. (2007). Base Points, Non-unit Implications, and Convex Geometries. In: Kuznetsov, S.O., Schmidt, S. (eds) Formal Concept Analysis. ICFCA 2007. Lecture Notes in Computer Science(), vol 4390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70901-5_14
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DOI: https://doi.org/10.1007/978-3-540-70901-5_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70828-5
Online ISBN: 978-3-540-70901-5
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