Simplifying Description Logic Ontologies

We discuss the problem of minimizing TBoxes expressed in the lightweight description logic $\mathcal{EL}$ , which forms a basis of some large ontologies like SNOMED, Gene Ontology, NCI and Galen. We show that the minimization of TBoxes is intractable (NP-complete). While this looks like a bad news result, we also provide a heuristic technique for minimizing TBoxes. We prove the correctness of the heuristics and show that it provides optimal results for a class of ontologies, which we define through an acyclicity constraint over a reference relation between equivalence classes of concepts. To establish the feasibility of our approach, we have implemented the algorithm and evaluated its effectiveness on a small suite of benchmarks.