Description Logics and Fuzzy Probability (bibtex)
by Lutz Schröder, Dirk Pattinson
Abstract:
Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth values. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we develop existing propositional logics of fuzzy probability into a full-blown description logic, and we show decidability of several variants of this logic under Lukasiewicz semantics. We obtain these results in a novel generic framework f fuzzy coalgebraic logic; this enables us to extend our results to logics that combine crisp ingredients including standard crisp roles and crisp numerical probabilities with fuzzy roles and fuzzy probabilities.
Reference:
Description Logics and Fuzzy Probability (Lutz Schröder, Dirk Pattinson), In International Joint Conference on Artificial Intelligence, IJCAI 2011 (Toby Walsh, ed.), pp. 1075–1081, AAAI Press; Menlo Park, CA, 2011. [preprint] (Oral and poster presentation)
Bibtex Entry:
@InProceedings{SchroderPattinson11,
  author = {Lutz Schr{\"o}der and Dirk Pattinson},
  title = {Description Logics and Fuzzy Probability},
  year = {2011},
  editor = {Toby Walsh},
  booktitle = {International Joint Conference on Artificial Intelligence, IJCAI 2011},
  publisher = {AAAI Press; Menlo Park, CA},
  keywords = {fuzzy logic coalgebra probability expectation lukasiewicz semantics complexity},
  comment = { <a href = "http://informatik.uni-bremen.de/~lschrode/papers/FuzzyCDL.pdf"> [preprint] </a>},
  pages     = {1075-1081},
  url        = {http://ijcai.org/papers11/Papers/IJCAI11-184.pdf},
  abstract = {Uncertainty and vagueness are pervasive phenomena in real-life
knowledge. They are supported in extended description logics
that adapt classical description logics to deal with numerical
probabilities or fuzzy truth values. While the two concepts are
distinguished for good reasons, they combine in the notion of
probably, which is ultimately a fuzzy qualification of
probabilities. Here, we develop existing propositional logics of
fuzzy probability into a full-blown description logic, and we show
decidability of several variants of this logic under Lukasiewicz
semantics. We obtain these results in a novel generic framework f
fuzzy coalgebraic logic; this enables us to extend our
results to logics that combine crisp ingredients including standard
crisp roles and crisp numerical probabilities with fuzzy roles and
fuzzy probabilities.},
  note = {Oral and poster presentation},
}
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