Definition:Language of Propositional Logic

Definition
There are a lot of different formal systems expressing propositional logic.

Although they vary wildly in complexity and even disagree (to some extent) on what expressions are valid, generally all of these use a compatible formal language.

This page defines the formal language of choice on.

We will use $\mathcal L_0$ to represent the formal language of propositional logic in what follows.

In order to define $\mathcal L_0$, it is necessary to specify:


 * An alphabet $\mathcal A$
 * A collation system with the unique readability property for $\mathcal A$
 * A formal grammar (which determines the WFFs of $\mathcal L_0$)

Currently at /Alphabet

Collation System
The collation system for the language of propositional logic is that of words and concatenation.

The unique readability property is verified on Unique Readability for Language of Propositional Logic.

Currently at /Formal Grammar

Also defined as
Since most authors concern themselves only with one formal system for propositional logic, they tend to refer to the whole formal system as propositional calculus.

In correspondence, a particular author may decide to use only a subset of the signs.

Generally, the other signs then are considered definitional abbreviations.

At we aim to incorporate all these different approaches, and thus we have come to let propositional calculus be only the formal language, assigning different names to all of the formal systems using this language.

If so desired, a generic such formal system may be addressed as a propositional calculus, but this has to be used with reluctance and caution.