Non-Gödel Negation Makes Unwitnessed Consistency Undecidable

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Non-Gödel Negation Makes Unwitnessed Consistency Undecidable

Stefan BorgwardtStefan Borgwardt,  Rafael PeñalozaRafael Peñaloza
Stefan Borgwardt, Rafael Peñaloza
Non-Gödel Negation Makes Unwitnessed Consistency Undecidable
In Yevgeny Kazakov and Domenico Lembo and Frank Wolter, eds., Proceedings of the 2012 International Workshop on Description Logics (DL'12), volume 846 of CEUR-WS, 411-421, 2012
  • KurzfassungAbstract
    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.
  • Forschungsgruppe:Research Group: Automatentheorie
@inproceedings{ BoPe-DL12,
  address = {Rome, Italy},
  author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}},
  booktitle = {Proceedings of the 2012 International Workshop on Description Logics ({DL'12})},
  editor = {Yevgeny {Kazakov} and Domenico {Lembo} and Frank {Wolter}},
  pages = {411--421},
  series = {CEUR-WS},
  title = {Non-{G{\"o}}del Negation Makes Unwitnessed Consistency Undecidable},
  volume = {846},
  year = {2012},
}