Fuzzy Description Logic Reasoning Using a Fixpoint Algorithm

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Fuzzy Description Logic Reasoning Using a Fixpoint Algorithm
We present FixIt(ALC), a novel procedure for deciding knowledge base (KB) satisfiability in the Fuzzy Description Logic (FDL) ALC. FixIt(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 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.
Uwe Keller, Stijn Heymans
Added 27 May 2010
Updated 27 May 2010
Type Conference
Year 2009
Where LFCS
Authors Uwe Keller, Stijn Heymans
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