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U. Keller, S. Heymans:
"Fuzzy Description Logic Reasoning using a Fixpoint Algorithm";
Vortrag: Symposium on Logical Foundations of Computer Science (LFCS), Deerfield Beach, Florida, U.S.A.; 03.01.2009 - 06.01.2009; in: "Proceedings of the Symposium on Logical Foundations of Computer Science (LFCS 2009)", Springer, 5407 (2009), ISBN: 978-3-540-92686-3; S. 265 - 279.

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, com-
pleteness 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 rea-
soning 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.

fuzzy Description Logics

http://dx.doi.org/10.1007/978-3-540-92687-0_18

http://publik.tuwien.ac.at/files/PubDat_167775.pdf