Efficient MUS Enumeration of Horn Formulae with Applications to Axiom Pinpointing

The enumeration of minimal unsatisfiable subsets (MUSes) finds a growing number of practical applications, that includes a wide range of diagnosis problems. As a concrete example, the problem of axiom pinpointing in the \(\mathcal {EL}\) family of description logics (DLs) can be modeled as the enumeration of the group-MUSes of Horn formulae. In turn, axiom pinpointing for the \(\mathcal {EL}\) family of DLs finds important applications, such as debugging medical ontologies, of which SNOMED CT is the best known example. The main contribution of this paper is to develop an efficient group-MUS enumerator for Horn formulae, HgMUS, that finds immediate application in axiom pinpointing for the \(\mathcal {EL}\) family of DLs. In the process of developing HgMUS, the paper also identifies performance bottlenecks of existing solutions. The new algorithm is shown to outperform all alternative approaches when the problem domain targeted by group-MUS enumeration of Horn formulae is axiom pinpointing for the \(\mathcal {EL}\) family of DLs, with a representative suite of examples taken from different medical ontologies.