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 $\LL_0$, 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

 $\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: