A fuzzy extension of description logic ALCH

Authors:
Yanhui Li;Jianjiang Lu;Baowen Xu;Dazhou Kang;Jixiang Jiang
Affiliations:
,Department of Computer Science and Engineering, Southeast University, Nanjing, P.R. China;,Department of Computer Science and Engineering, Southeast University, Nanjing, P.R. China;,Department of Computer Science and Engineering, Southeast University, Nanjing, P.R. China;,Department of Computer Science and Engineering, Southeast University, Nanjing, P.R. China;,Department of Computer Science and Engineering, Southeast University, Nanjing, P.R. China
Venue:
MICAI'05 Proceedings of the 4th Mexican international conference on Advances in Artificial Intelligence
Year:
2005

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Abstract

Based on the idea that the cut sets of fuzzy sets are indeed crisp, but facilitate a normative theory for formalizing fuzzy set theory, this paper introduces cut sets of the fuzzy concepts and fuzzy roles as atomic concepts and atomic roles to build $\mathcal{EFALCH}$ , a new fuzzy extension of $\mathcal{ALCH}$. This paper gives the definition of syntax, semantics and knowledge base of $\mathcal{EFALCH}$ and discusses the comparison among $\mathcal{EFALCH}$ and other fuzzy extensions of $\mathcal{ALCH}$. In addition, this paper defines the acyclic TBox form of $\mathcal{EFALCH}$, presents sound and complete algorithms for reasoning tasks w.r.t acyclic TBox, and proves the complexity of them is PSPACE-complete.