Fuzzy description logic reasoning using a fixpoint algorithm

Abstract

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. © Springer-Verlag Berlin Heidelberg 2009.