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Applied Computational Intelligence and Soft Computing
Volume 2010, Article ID 907298, 7 pages
Research Article

Consistency Degrees of Theories in Łukasiewicz Fuzzy and -Valued Propositional Logic Systems

Department of Mathematics, Quanzhou Normal University, Quanzhou, Fujian 362000, China

Received 7 October 2009; Revised 28 January 2010; Accepted 31 May 2010

Academic Editor: Etienne Kerre

Copyright © 2010 Jiancheng Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By means of theory of truth degrees of formulas, according to deduction theorems and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Łukasewicz fuzzy and -valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theory to be consistent, inconsistent, and fully divergent are obtained. Finally, some important properties of truth degrees of formulas are proposed.