Definition:Variable/Propositional Logic

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Definition

A statement variable is a variable which is used to stand for arbitrary and unspecified statements.


For statement variables, lowercase letters are usually used, e.g.:

$p, q, r, \ldots{}$, etc.

or lowercase Greek letters, e.g.:

$\phi, \psi, \chi$ etc.


The citing of a variable can be interpreted as an assertion that the statement represented by that symbol is true.

That is:

$p$

means

$p \text { is true}$


Also known as

Equivalent terms for statement variable are:

  • sentential variable
  • propositional variable
  • proposition symbol.

The latter name is also used for the letters of the language of propositional logic, which are intended to represent statement variables.


Also see

Note the difference between a statement label and a statement variable.

The first is used to identify a particular statement. The latter is used to represent an instance of any statement at all.


Sources