Definition:Language of Propositional Logic/Alphabet

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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:


Sources