Mining EL Bases with Adaptable Role Depth

TL;DR

This paper introduces an adaptable method for mining EL bases in Description Logic that dynamically bounds role depth based on local interpretation structure, ensuring all valid concept inclusions are captured.

Contribution

It presents a novel strategy for mining EL bases with adaptable role depth, improving over fixed-depth approaches by capturing all valid inclusions.

Findings

Guarantees to find all EL concept inclusions in an interpretation.

Adapts role depth based on local structure.

Ensures completeness of the mined base.

Abstract

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining EL bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining EL bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all EL concept inclusions holding in the interpretation, not only the ones up to a fixed role depth.