Forgetting in General EL Terminologies

Recently, different forgetting approaches for knowledge bases expressed in different logics were proposed. For EL terminologies containing each atomic concept at most once on the left-hand side, an approach has been proposed based on sufficient, but not necessary acyclicity conditions. In this paper, we propose an approach for computing a uniform interpolant for general EL terminologies. We first show that a uniform interpolant of any EL terminology w.r.t. any signature always exists in EL enriched with least and greatest fixpoint constructors and show how it can be computed by reducing the problem to the computation of Most General Subconcepts and Most Specific Superconcepts for atomic concepts. Then, we give the exact conditions for the existence of a uniform interpolant in EL and show how it can be obtained using our algorithms.