  The EL family of Description Logics (DLs) has been the subject of interest in
recent years. On the one hand, these DLs are tractable, but fairly
inexpressive. On the other hand, these DLs can be used for designing different
classes of ontologies, most notably ontologies from the medical domain.
Unfortunately, building ontologies is error-prone. As a result, inferable
subsumption relations among concepts may be unintended. In recent years, the
problem of axiom pinpointing has been studied with the purpose of providing
minimal sets of axioms that explain unintended subsumption relations. For the
concrete case of EL and EL+, the most efficient approaches consist of encoding
the problem into propositional logic, specifically as a Horn formula, which is
then analyzed with a dedicated algorithm. This paper builds on this earlier
work, but exploits the important relationship between minimal axioms sets and
minimal unsatisfiable subformulas in the propositional domain. In turn, this
relationship allows applying a vast body of recent work in the propositional
domain to the concrete case of axiom pinpointing for EL and its variants. From
a practical perspective, the algorithms described in this paper are often
several orders of magnitude more efficient that the current state of the art in
axiom pinpointing for the EL family of DLs.
