Abstract
By adding new operators \(\varDelta \) and \(\sim \), axiomatic expansion of \(G\ddot{o}del\) n-valued propositional logic system is introduced, which is denoted by \(G\ddot{o}del_{\sim }\). In this paper, the concept of t truth degree of propositional formula is put forward in \(G\ddot{o}del_{\sim }\) (t take \(\varDelta , \sim \)), and the MP rule, HS rule and some related properties are studied; the concepts of t similarity degree, t pseudo-metric between propositional formulas, and t divergent degree and t consistent degree of theory \(\varGamma \) in \(G\ddot{o}del_{\sim }\) are obtained, and their correlation properties are discussed.
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Project Supported by the National Natural Science Foundation of China under Grant (11471007); the Natural Science Foundation of Shaanxi Province under Grant (2014JM1020); Graduate Innovation Fund of Yan’an University (YCX201612).
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Zhu, ND., Hui, XJ., Gao, XL. (2017). A New Theory of T Truth Degree on \({\text {G}}\ddot{\text {o}}{\text {del}}\) n-Valued Propositional Logic System. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_7
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DOI: https://doi.org/10.1007/978-3-319-46206-6_7
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