Definability in Logic and Rough Set Theory

Authors:
Tuan-Fang Fan;Churn-Jung Liau;Duen-Ren Liu
Affiliations:
Dept. of Comp. Sci. and Info. Eng., National Penghu Univ., Penghu 880, Taiwan, email: dffan@npu.edu.tw and Institute of Information Management, National Chiao-Tung University, Hsinchu 300, Taiwan, ...;Institute of Information Science, Academia Sinica, Taipei 115, Taiwan, email: liaucj@iis.sinica.edu.tw;Institute of Information Management, National Chiao-Tung University, Hsinchu 300, Taiwan, email: dliu@iim.nctu.edu.tw
Venue:
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Year:
2008

Citing 3
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Abstract

Rough set theory is an effective tool for data mining. According to the theory, a concept is definable if it can be written as a Boolean combination of equivalence classes induced from classification attributes. On the other hand, definability in logic has been explicated by Beth's theorem. In this paper, we propose two data representation formalisms, called first-order data logic (FODL) and attribute value-sorted logic (AVSL), respectively. Based on these logics, we explore the relationship between logical definability and rough set definability.