# Boolean Substructures in Formal Concept Analysis

arXiv: https://arxiv.org/abs/2104.07159 · HTML: https://mlsanity.com/paper/2104.07159/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [Attribute Selection using Contranominal Scales](https://mlsanity.com/paper/2106.10978/) (2021)

## Abstract (arXiv)

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.