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标题：Consistency Degrees of Theories in Łukasiewicz Fuzzy and <svg style="vertical-align:-0.144pt;width:12.38625px;" id="M1" height="11.31" version="1.1" viewBox="0 0 12.38625 11.31" width="12.38625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.31)"> <text transform="matrix(1,0,0,-1,0.498,0.642)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑛</tspan> </text> </g> </svg>-Valued Propositional Logic Systems
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作者：Jiancheng Zhang
期刊名称：Applied Computational Intelligence and Soft Computing
印刷版ISSN：1687-9724
电子版ISSN：1687-9732
出版年度：2010
卷号：2010
DOI：10.1155/2010/907298
出版社：Hindawi Publishing Corporation
摘要：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 𝑛-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theory Γ to be consistent, inconsistent, and fully divergent are obtained. Finally, some important properties of truth degrees of formulas are proposed.