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Uniform Interpolation in General EL Terminologies

Published: 2011 Mai
Institution: Institut AIFB, KIT
Erscheinungsort / Ort: Karlsruhe
BibTex-ID: nikitina2011c

Recently, non-standard reasoning problems have gained the attention from the research community. Amongst others, different forgetting (or uniform interpolation) approaches for knowledge bases expressed in different logics were proposed. It was shown that the result may not exist in the presence of terminological cycles and sufficient, but not necessary conditions for its existence were proposed. In this paper, we 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. Moreover, we give the exact conditions for the existence of a uniform interpolant in EL and show how it can be obtained using our algorithms.

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