二值谓词逻辑中公式的向量真度*

摘要

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.%首次将谓词逻辑系统中一阶语言的有限解释按照其论域的势进行分层，提出每一层解释类下公式的n真度，最终给出公式向量真度的定义，更直观精确地刻画一阶公式的真实程度。接着证明向量真度的一些基本性质，指出向量真度保持谓词逻辑形式推理的MP规则、HS规则与推广规则，从而为进一步在谓词逻辑系统中开展近似推理研究提供一种可能的框架。