Consistency reasoning in lattice-based fuzzy description logics
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Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known about the complexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in this paper we study the consistency problem for the fuzzy Description Logic L-SHI and its sublogics in detail. The contribution of the paper is twofold. On the one hand, we provide a tableaux-based algorithm for deciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed for classical SHI. On the other hand, we identify decidable and undecidable classes of fuzzy Description Logics over infinite lattices. For all the decidable classes, we also provide tight complexity bounds.
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Borgwardt, S; Penaloza, R (Springer, 2013)We study the complexity of reasoning in fuzzy description logics with semantics based on finite residuated lattices. For the logic SHI, we show that deciding satisfiability and subsumption of concepts, with or without a ...
Borgwardt, S; Distel, F; Penaloza, R (Springer-Verlag, 2012)Fuzzy Description Logics (DLs) with t-norm semantics have been studied as a means for representing and reasoning with vague knowledge. Recent work has shown that even fairly inexpressive fuzzy DLs become undecidable for a ...
Borgwardt, S; Leyva, Galano JA; Penaloza, R (Springer-Verlag, 2014)We study the fuzzy extension of the Description Logic FL0 with semantics based on the Gödel t-norm. We show that subsumption w.r.t. a finite set of primitive definitions, using greatest fixed-point semantics, can be ...