Reasoning for a fuzzy description logic with comparison expressions.pdf

Reasoning for A Fuzzy Description Logic with Comparison Expressions ? Dazhou Kang1, Baowen Xu1,2, Jianjiang Lu3 and Yanhui Li1 1School of Computer Science and Engineering, Southeast University, Nanjing 210096, China 2Jiangsu Institute of Software Quality, Nanjing, 210096, China 3Institute of Command Automation, PLA University of Science and Technology, Nanjing 210007, China Abstract The fuzzy extensions of description logics support representation and reasoning for fuzzy knowledge. But the current fuzzy description logics do not support the expression of comparisons between fuzzy membership degrees. The paper proposes ALCfc, a fuzzy extension of description logic ALC with comparison expressions. ALCfc defines comparison cut concepts to express complex comparisons, and integrate them with fuzzy ALC. The challenges of reasoning in ALCfc is discussed, and a tableau algorithm is presented. It enables representation and reasoning for ex- pressive fuzzy knowledge about comparisons. 1 Introduction Description logics (DLs) [1] are widely used in the semantic web. Fuzzy exten- sions of description logics import the fuzzy theory to enable the capability of dealing with fuzzy knowledge [5]. In fuzzy DLs, an individual is an instance of a fuzzy concept only to a certain degree (called fuzzy membership degree); e.g. “Tom is tall to a degree greater than 0.8,” where Tall is a fuzzy concept. It is also a familiar description that “Tom is taller than Mike,” which can be seemed as a comparison between two degrees without any restrictions on their exact ?This work was supported by NSFC and, National Grand Fundamental Research 973 Program of China (2002CB312000), Innovation Plan for Jiangsu High School Graduate Student, Advanced Armament Research Project (51406020105JB8103), Advanced Research Fund of Southeast University (XJ0609233), and High Technology Research Project of Jiangsu Province (BG2005032). Email:swws@seu.edu.cn values. Such comparison is impo