# Definition:Language of Propositional Logic/Alphabet

## Definition

The alphabet $\AA$ of the language of propositional logic $\LL_0$ is defined as follows:

### Letters

The letters of $\LL_0$, called propositional symbols, can be any infinite collection $\PP_0$ of arbitrary symbols.

It is usual to specify them as a limited subset of the English alphabet with appropriate subscripts.

A typical set of propositional symbols would be, for example:

$\PP_0 = \set {p_1, p_2, p_3, \ldots, p_n, \ldots}$

### Signs

The signs of the language of propositional logic come in two categories:

#### Brackets

 $\ds \bullet \ \$ $\ds ($ $:$ $\ds$the left bracket sign $\ds \bullet \ \$ $\ds )$ $:$ $\ds$the right bracket sign

#### Connectives

 $\ds \bullet \ \$ $\ds \land$ $:$ $\ds$the conjunction sign $\ds \bullet \ \$ $\ds \lor$ $:$ $\ds$the disjunction sign $\ds \bullet \ \$ $\ds \implies$ $:$ $\ds$the conditional sign $\ds \bullet \ \$ $\ds \iff$ $:$ $\ds$the biconditional sign $\ds \bullet \ \$ $\ds \neg$ $:$ $\ds$the negation sign $\ds \bullet \ \$ $\ds \top$ $:$ $\ds$the tautology sign $\ds \bullet \ \$ $\ds \bot$ $:$ $\ds$the contradiction sign

These comprise: