On the Undecidability of Fuzzy Description Logics with GCIs and Product t-norm

Franz BaaderFranz Baader, Rafael PeñalozaRafael Peñaloza

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Franz Baader, Rafael Peñaloza
On the Undecidability of Fuzzy Description Logics with GCIs and Product t-norm
In Cesare Tinelli and Viorica Sofronie-Stokkermans, eds., Proceedings of 8th International Symposium Frontiers of Combining Systems (FroCoS 2011), volume 6989 of Lecture Notes in Aritificial Intelligence, 55-70, 2011. Springer

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KurzfassungAbstract
The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. Recently, it has been shown that, in the presence of general concept inclusion axioms (GCIs), some of these fuzzy DLs actually do not have the finite model property, thus throwing doubt on the correctness of tableau algorithm for which it was claimed that they can handle fuzzy DLs with GCIs. In a previous paper, 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 the present paper, we show that undecidability also holds if we consider a t-norm-based fuzzy DL where disjunction and involutive negation are replaced by the constructor implication, which is interpreted as the residuum. The only condition on the t-norm is that it is a continuous t-norm "starting" with the product t-norm, which covers an uncountable family of t-norms.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

The final publication is available at Springer.

@inproceedings{ BaPe-FroCoS11,
  address = {Saarbr{\"u}cken, Germany},
  author = {Franz {Baader} and Rafael {Pe{\~n}aloza}},
  booktitle = {Proceedings of 8th International Symposium Frontiers of Combining Systems ({FroCoS 2011})},
  editor = {Cesare {Tinelli} and Viorica {Sofronie-Stokkermans}},
  pages = {55--70},
  publisher = {Springer-Verlag},
  series = {Lecture Notes in Aritificial Intelligence},
  title = {On the Undecidability of Fuzzy Description Logics with GCIs and Product t-norm},
  volume = {6989},
  year = {2011},
}