Definition:Variable/Propositional Logic

Definition

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

For a statement variable, a lowercase letter is usually used, for example:

$p, q, r, \ldots{}$, and so on

or lowercase Greek letters, for example:

$\phi, \psi, \chi$ and so on.

The citing of a statement 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 or propositional 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

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