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, 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.

Also see

 * Definition:Sign of Propositional Logic
 * Definition:Connective of Propositional Logic


 * Definition:Statement Variable: when symbolic logic is presented less precisely than in the context of a formal language, the alphabet from which its symbols may be taken is often not specified.