Recent results show that ontology consistency is undecidable for a wide variety of fuzzy Description Logics (DLs). Most notably, undecidability arises for a family of inexpressive fuzzy DLs using only conjunction, existential restrictions, and residual negation, even if the ontology itself is crisp. All those results depend on restricting reasoning to witnessed models. In this paper, we show that ontology consistency for inexpressive fuzzy DLs using any t-norm starting with the Łukasiewicz t-norm is also undecidable w.r.t. general models.

Borgwardt, S., Peñaloza, R. (2012). Non-Gödel Negation Makes Unwitnessed Consistency Undecidable. In Proceedings of the 2012 International Workshop on Description Logics, June 7-10, 2012, Rome, Italy (pp.411-421). CEUR.

Non-Gödel Negation Makes Unwitnessed Consistency Undecidable

Peñaloza, R
2012

Abstract

Recent results show that ontology consistency is undecidable for a wide variety of fuzzy Description Logics (DLs). Most notably, undecidability arises for a family of inexpressive fuzzy DLs using only conjunction, existential restrictions, and residual negation, even if the ontology itself is crisp. All those results depend on restricting reasoning to witnessed models. In this paper, we show that ontology consistency for inexpressive fuzzy DLs using any t-norm starting with the Łukasiewicz t-norm is also undecidable w.r.t. general models.
paper
fuzzy logic, description logics
English
International Workshop on Description Logics (DL 2012)
2012
Kazakov, Y; Lembo, D; Wolter, F
Proceedings of the 2012 International Workshop on Description Logics, June 7-10, 2012, Rome, Italy
2012
846
411
421
open
Borgwardt, S., Peñaloza, R. (2012). Non-Gödel Negation Makes Unwitnessed Consistency Undecidable. In Proceedings of the 2012 International Workshop on Description Logics, June 7-10, 2012, Rome, Italy (pp.411-421). CEUR.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/257705
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