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

Borgwardt, S., Penaloza Nyssen, R. (2014). Consistency reasoning in lattice-based fuzzy description logics. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 55(9), 1917-1938 [10.1016/j.ijar.2013.07.006].

Consistency reasoning in lattice-based fuzzy description logics

Penaloza Nyssen, R
2014

Abstract

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
Articolo in rivista - Articolo scientifico
fuzzy logic, description logics
English
2014
55
9
1917
1938
open
Borgwardt, S., Penaloza Nyssen, R. (2014). Consistency reasoning in lattice-based fuzzy description logics. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 55(9), 1917-1938 [10.1016/j.ijar.2013.07.006].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/258731
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