Goedel Description Logics: Decidability in the Absence of the Finitely-Valued Model Property

Stefan BorgwardtStefan Borgwardt, Felix DistelFelix Distel, Rafael PeñalozaRafael Peñaloza

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Stefan Borgwardt, Felix Distel, Rafael Peñaloza
Goedel Description Logics: Decidability in the Absence of the Finitely-Valued Model Property
Technical Report, Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden, volume 13-09, 2013. LTCS-Report

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KurzfassungAbstract
In the last few years there has been a large effort for analysing the computational properties of reasoning in fuzzy Description Logics. This has led to a number of papers studying the complexity of these logics, depending on their chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy DLs w.r.t. witnessed models over the Goedel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely-valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in this logic in exponential time, matching the complexity of reasoning in classical ALC.
Bemerkung: Note: See http://lat.inf.tu-dresden.de/research/reports.html.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@techreport{ BoDP-LTCS-13-09,
  address = {Dresden, Germany},
  author = {Stefan {Borgwardt} and Felix {Distel} and Rafael {Pe{\~n}aloza}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html.},
  number = {13-09},
  title = {Goedel Description Logics: Decidability in the Absence of the Finitely-Valued Model Property},
  type = {LTCS-Report},
  year = {2013},
}