DeepAI AI Chat
Log In Sign Up

Factorizing Lattices by Interval Relations

12/20/2022
by   Maren Koyda, et al.
Universität Kassel
0

This work investigates the factorization of finite lattices to implode selected intervals while preserving the remaining order structure. We examine how complete congruence relations and complete tolerance relations can be utilized for this purpose and answer the question of finding the finest of those relations to implode a given interval in the generated factor lattice. To overcome the limitations of the factorization based on those relations, we introduce a new lattice factorization that enables the imploding of selected disjoint intervals of a finite lattice. To this end, we propose an interval relation that generates this factorization. To obtain lattices rather than arbitrary ordered sets, we restrict this approach to so-called pure intervals. For our study, we will make use of methods from Formal Concept Analysis (FCA). We will also provide a new FCA construction by introducing the enrichment of an incidence relation by a set of intervals in a formal context, to investigate the approach for lattice-generating interval relations on the context side.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/02/2022

Interval-Dismantling for Lattices

Dismantling allows for the removal of elements of a set, or in our case ...
04/14/2021

Boolean Substructures in Formal Concept Analysis

It is known that a (concept) lattice contains an n-dimensional Boolean s...
02/07/2022

Non-traditional intervals and their use. Which ones really make sense?

The paper discusses the question of why intervals, which are the main ob...
06/09/2020

The Hitchhiker's Guide to the All-Interval 12-Tone Rows

This article revisits the generation, classification and categorization ...
04/05/2018

A Proof of the Compositions of Time Interval Relations

We prove the 169 compositions of time interval relations. The proof is f...
09/12/2018

An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part II)

There are two natural and well-studied approaches to temporal ontology a...
06/04/2018

Efficient Genomic Interval Queries Using Augmented Range Trees

Efficient large-scale annotation of genomic intervals is essential for p...