GCIs Make Reasoning in Fuzzy DL with the Product T-norm Undecidable

Franz BaaderFranz Baader, Rafael PeñalozaRafael Peñaloza

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Franz Baader, Rafael Peñaloza
GCIs Make Reasoning in Fuzzy DL with the Product T-norm Undecidable
In Riccardo Rosati and Sebastian Rudolph and Michael Zakharyaschev, eds., Proceedings of the 24th International Workshop on Description Logics (DL 2011), volume 745 of CEUR-WS, 2011

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KurzfassungAbstract
Fuzzy Description Logics (DLs) have been investigated for at least two decades because they can be used to formalize imprecise concepts. In particular, tableau algorithm for crisp DLs have been extended to reason also with their fuzzy counterparts. Recently, it has been shown that, in the presence of GCIs, some of these fuzzy DLs do not have the finite model property, thus throwing doubt on the correctness of tableau algorithms claimed to handle fuzzy DLs with GCIs. Previously, we have shown that these doubts are indeed justified, by proving that a certain fuzzy DL with product t-norm and involutive negation is undecidable. In this paper, we show that undecidability also holds if we consider a fuzzy DL where disjunction and involutive negation are replaced by the constructor implication, interpreted as the residuum.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@inproceedings{ BaPe-DL11,
  address = {Barcelona, Spain},
  author = {Franz {Baader} and Rafael {Pe{\~n}aloza}},
  booktitle = {Proceedings of the 24th International Workshop on Description Logics (DL 2011)},
  editor = {Riccardo {Rosati} and Sebastian {Rudolph} and Michael {Zakharyaschev}},
  series = {CEUR-WS},
  title = {GCIs Make Reasoning in Fuzzy DL with the Product T-norm Undecidable},
  volume = {745},
  year = {2011},
}