Connection-minimal Abduction in EL via Translation to FOL -- Technical Report
This work addresses the problem of generating meaningful explanations in knowledge bases for applications like knowledge repair, but it is incremental as it builds on existing abduction methods with a new minimality criterion.
The paper tackles TBox abduction in the EL description logic by introducing connection minimality to avoid useless hypotheses, and shows how to compute these hypotheses using a translation to first-order logic and prime implicates, with evaluation on medical ontologies.
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.