# 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.