Vector Truth Degrees of Formulae in Two-Valued Predicate Logic
QIN Xiao-Yan1, 2, XU Yang1, LIU Yi1
1. Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031
2. College of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004
All of the finite interpretations of first-order languages are considered in layers according to their cardinalities for the first time, and n-truth degrees of formulae under each layer of the class of interpretations are proposed.Then, the definition of the vector truth degrees of formulae is given to describe the truth degrees of first-order formulae more intuitively and more accurately. Moreover, some basic properties are proved, and it is pointed out that the vector truth degrees of formulae preserve Modus Ponens(MP) rule, Hypothetical Syllogism(HS) rule and rule of generalization(Gen) of the formal reasoning in the predicate logic. Thus, a kind of possible frame for approximate reasoning in predicate logic system is provided.
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2013, Vol. 26 
