The Distributive, Graded Lattice of EL Concept Descriptions and its Neighborhood Relation (Extended Version)

01/17/2019
by   Francesco Kriegel, et al.
0

For the description logic EL, we consider the neighborhood relation which is induced by the subsumption order, and we show that the corresponding lattice of EL concept descriptions is distributive, modular, graded, and metric. In particular, this implies the existence of a rank function as well as the existence of a distance function.

READ FULL TEXT
07/24/2019

A General Theory of Concept Lattice (I): Emergence of General Concept Lattice

As the first part of the treatise on A General Theory of Concept Lattice...
11/03/2018

The IFF Approach to the Lattice of Theories

The IFF approach for the notion of "lattice of theories" uses the idea o...
03/02/2023

Enumeration and Unimodular Equivalence of Empty Delta-Modular Simplices

Consider a class of simplices defined by systems A x ≤ b of linear inequ...
02/10/2018

A sequence of neighborhood contingency logics

This note proposes various axiomatizations of contingency logic under ne...
04/07/2022

Two flags in a semimodular lattice generate an antimatroid

A basic property in a modular lattice is that any two flags generate a d...
09/24/2018

A family of neighborhood contingency logics

This article proposes the axiomatizations of contingency logics of vario...
09/27/2022

Strategyproofness-Exposing Mechanism Descriptions

A menu description defines a mechanism to player i in two steps. Step (1...

Please sign up or login with your details

Forgot password? Click here to reset