Boolean Substructures in Formal Concept Analysis
Discrete Mathematics
2021-04-16 v1 Logic in Computer Science
Abstract
It is known that a (concept) lattice contains an n-dimensional Boolean suborder if and only if the context contains an n-dimensional contra-nominal scale as subcontext. In this work, we investigate more closely the interplay between the Boolean subcontexts of a given finite context and the Boolean suborders of its concept lattice. To this end, we define mappings from the set of subcontexts of a context to the set of suborders of its concept lattice and vice versa and study their structural properties. In addition, we introduce closed-subcontexts as an extension of closed relations to investigate the set of all sublattices of a given lattice.
Cite
@article{arxiv.2104.07159,
title = {Boolean Substructures in Formal Concept Analysis},
author = {Maren Koyda and Gerd Stumme},
journal= {arXiv preprint arXiv:2104.07159},
year = {2021}
}