Abstract
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.
This work has been partially funded by the European Commission under the LarKC project (FP7 - 215535). Stijn Heymans is supported by the Austrian Science Fund (FWF) under projects P20305 and P20840.
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Keller, U., Heymans, S. (2008). Fuzzy Description Logic Reasoning Using a Fixpoint Algorithm. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2009. Lecture Notes in Computer Science, vol 5407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92687-0_18
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