Consistency Reasoning in Lattice-Based Fuzzy Description Logics

Stefan BorgwardtStefan Borgwardt, Rafael PeñalozaRafael Peñaloza

Stefan Borgwardt, Rafael Peñaloza
Consistency Reasoning in Lattice-Based Fuzzy Description Logics
International Journal of Approximate Reasoning, 55(9):1917-1938, 2014

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KurzfassungAbstract
Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known about the complexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in this paper we study the consistency problem for the fuzzy Description Logic L-SHI and its sublogics in detail. The contribution of the paper is twofold. On the one hand, we provide a tableaux-based algorithm for deciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed for classical SHI. On the other hand, we identify decidable and undecidable classes of fuzzy Description Logics over infinite lattices. For all the decidable classes, we also provide tight complexity bounds.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@article{ BoPe-IJAR14,
  author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}},
  doi = {http://dx.doi.org/10.1016/j.ijar.2013.07.006},
  journal = {International Journal of Approximate Reasoning},
  number = {9},
  pages = {1917--1938},
  title = {Consistency Reasoning in Lattice-Based Fuzzy Description Logics},
  volume = {55},
  year = {2014},
}