# Definition:Language of Propositional Logic/Alphabet/Letter

## Definition

Part of specifying the language of propositional logic $\LL_0$ is to specify its 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:

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

## Also defined as

Some sources do not specify that $\PP_0$ be infinite.

However, since one can simply "forget to use" all but finitely many letters, this does not provide a more general theory.

## Also known as

Propositional symbols are also known as the propositional variables of $\LL_0$.

Others call them atomic propositions or simply atoms.

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$, atom has a broader context, and so is discouraged as an alternative for propositional symbol.

Some sources refer to the collection of letters as the vocabulary of the language.