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命题变量

数理逻辑中,命题变量(也称命题变元句子变量)是要么为要么为变量。命题变量是命题公式的基本构件板块,用于命题逻辑和更高的逻辑中。

逻辑中的公式通常是由一些命题变量、一些逻辑连接词和一些逻辑量词递归地建立的。命题变量是命题逻辑的原子公式,通常用大写字母表示,如

在一个给定的命题逻辑中,我们可以按如下方式定义公式:

  • 所有命题变量是公式。
  • 给定公式 否定 是公式。
  • 给定两个公式 ,和一个二元连结词 (比如逻辑合取 ),则 是公式。

通过上述方式,命题逻辑的所有公式都可以通过作为基本单位的命题变量构造出来。

引用

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Smullyan, Raymond M. First-Order Logic. 1968. Dover edition, 1995. Chapter 1.1: Formulas of Propositional Logic.

参见

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命题变量
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