  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.
