Base points, non-unit implications, and convex geometries

Authors:
Bernhard Ganter;Heiko Reppe
Affiliations:
Institute for Algebra, Dresden University of Technology, Dresden;Institute for Algebra, Dresden University of Technology, Dresden
Venue:
ICFCA'07 Proceedings of the 5th international conference on Formal concept analysis
Year:
2007

Citing 2
Cited 1

Formal Concept Analysis: Mathematical Foundations

Formal Concept Analysis: Mathematical Foundations
About the family of closure systems preserving non-unit implications in the guigues-duquenne base

ICFCA'06 Proceedings of the 4th international conference on Formal Concept Analysis

Attribute Exploration Using Implications with Proper Premises

ICCS '08 Proceedings of the 16th international conference on Conceptual Structures: Knowledge Visualization and Reasoning

Quantified Score

Hi-index	0.00

Visualization

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.