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.
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