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

 * Definition:Statement Label: Note the difference between this and a statement variable:
 * The first is used to identify a particular statement.
 * The latter is used to represent an arbitrary instance of any statement at all.


 * Definition:Propositional Symbol: when propositional logic is developed as a formal language, a statement variable is specified precisely.