Connection-minimal Abduction in EL via Translation to FOL -- Technical Report

TL;DR

This paper introduces connection minimality for TBox abduction in EL, using a translation to first-order logic to compute hypotheses that are relevant and minimal, with applications in medical ontologies.

Contribution

It proposes a novel connection minimality criterion for TBox abduction in EL and a translation-based method to compute such hypotheses.

Findings

The approach is sound and complete for a class of hypotheses.

Prototype implementation shows effectiveness on medical ontologies.

Connection minimality improves relevance of explanations.

Abstract

Abduction in description logics finds extensions of a knowledge base to make it entail an observation. As such, it can be used to explain why the observation does not follow, to repair incomplete knowledge bases, and to provide possible explanations for unexpected observations. We consider TBox abduction in the lightweight description logic EL, where the observation is a concept inclusion and the background knowledge is a TBox, i.e., a set of concept inclusions. To avoid useless answers, such problems usually come with further restrictions on the solution space and/or minimality criteria that help sort the chaff from the grain. We argue that existing minimality notions are insufficient, and introduce connection minimality. This criterion follows Occam's razor by rejecting hypotheses that use concept inclusions unrelated to the problem at hand. We show how to compute a special class of connection-minimal hypotheses in a sound and complete way. Our technique is based on a translation to first-order logic, and constructs hypotheses based on prime implicates. We evaluate a prototype implementation of our approach on ontologies from the medical domain.