Logical Foundations of Computer Science

Volume 5407 of the series Lecture Notes in Computer Science pp 265-279

Fuzzy Description Logic Reasoning Using a Fixpoint Algorithm

  • Uwe KellerAffiliated withSemantic Technology Institute (STI) Innsbruck, University of Innsbruck
  • , Stijn HeymansAffiliated withKnowledge-based Systems Group, Institute of Information Systems, Vienna University of Technology

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We present \({\mathbf{FixIt}}{\mathbb{(ALC)}}\), a novel procedure for deciding knowledge base (KB) satisfiability in the Fuzzy Description Logic (FDL) \({\mathbb{ALC}}\). \({\mathbf{FixIt}}{\mathbb{(ALC)}}\) does not search for tree-structured models as in tableau-based proof procedures, but embodies a (greatest) fixpoint-computation of canonical models that are not necessarily tree-structured, based on a type-elimination process. Soundness, completeness and termination are proven and the runtime and space complexity are discussed. We give a precise characterization of the worst-case complexity of deciding KB satisfiability (as well as related terminological and assertional reasoning tasks) in \({\mathbb{ALC}}\) in the general case and show that our method yields a worst-case optimal decision procedure (under reasonable assumptions). To the best of our knowledge it is the first fixpoint-based decision procedure for FDLs, hence introducing a new class of inference procedures into FDL reasoning.