Techreport3017: Unterschied zwischen den Versionen

Version vom 9. Mai 2011, 10:54 Uhr

Uniform Interpolation in General EL Terminologies

Published: 2011 Mai
Institution: Institut AIFB, KIT
Erscheinungsort / Ort: Karlsruhe
Archivierungsnummer:3017

Kurzfassung
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.

Projekt

NanOn

Forschungsgruppe

Wissensmanagement

Forschungsgebiet

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 {{Publikation Details
-|Abstract=Recently, non-standard reasoning problems have gained the attention from the research community. Amongst others, different approaches to computing the Uniform Interpolation for concepts and knowledge bases expressed in $\mathcal{H}$orn extensions of $\mathcal{EL}$ were proposed. Further, it was shown, that Uniform Interpolation may not exist in the presence of terminological cycles and sufficient, but not necessary conditions for its existence in general terminologies were identified. The aim of this paper is to investigate, using the example of the Uniform Interpolation in $\mathcal{EL}$, the existence of the result for a particular class of non-standard reasoning problems in $\mathcal{EL}$ and some of its $\mathcal{H}$orn
+|Abstract=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.
-extensions. In this paper, we show that the Uniform Interpolation always exists in $\mathcal{EL}$ enriched with least and greatest fixpoint constructors and show how it can be computed by reducing the problem to the computation of most general subconcept and most specific superconcept. Moreover, we give the conditions for the existence of the Uniform Interpolation in $\mathcal{EL}$ and provide a complete algorithm for its computation.
 |Projekt=NanOn
 |Forschungsgruppe=Wissensmanagement
 }}