# Algorithms for Reasoning in Very Expressive Description Logics under Infinitely Valued Gödel Semantics

##### Stefan BorgwardtStefan Borgwardt,  Rafael PeñalozaRafael Peñaloza
Stefan Borgwardt, Rafael Peñaloza
Algorithms for Reasoning in Very Expressive Description Logics under Infinitely Valued Gödel Semantics
International Journal of Approximate Reasoning, 83:60–101, 2017
• KurzfassungAbstract
Fuzzy description logics (FDLs) are knowledge representation formalisms capable of dealing with imprecise knowledge by allowing intermediate membership degrees in the interpretation of concepts and roles. One option for dealing with these intermediate degrees is to use the so-called Gödel semantics, under which conjunction is interpreted by the minimum of the degrees of the conjuncts. Despite its apparent simplicity, developing reasoning techniques for expressive FDLs under this semantics is a hard task. In this paper, we introduce two new algorithms for reasoning in very expressive FDLs under Gödel semantics. They combine the ideas of a previous automata-based algorithm for Gödel FDLs with the known crispification and tableau approaches for FDL reasoning. The results are the two first practical algorithms capable of reasoning in infinitely valued FDLs supporting general concept inclusions.
• Projekt:Project: CfaedHAECHAEC B02
• Forschungsgruppe:Research Group: Automatentheorie
```@article{BP2017,
author  = {Stefan Borgwardt and Rafael Pe{\~{n}}aloza},
title   = {Algorithms for Reasoning in Very Expressive Description Logics
under Infinitely Valued G{\"{o}}del Semantics},
journal = {International Journal of Approximate Reasoning},
volume  = {83},
year    = {2017},
pages   = {60{\textendash}101},
doi     = {10.1016/j.ijar.2016.12.014}
}
```