# Definition:Language of Propositional Logic/Alphabet

## Definition

The alphabet $\mathcal A$ of the language of propositional logic $\mathcal L_0$ is defined as follows:

### Letters

The letters of $\mathcal L_0$, called propositional symbols, can be any infinite collection $\mathcal P_0$ 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:

$\mathcal P_0 = \left\{{p_1, p_2, p_3, \ldots, p_n, \ldots}\right\}$

### Signs

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

#### Brackets

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

#### Connectives

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

These comprise: