Definition:Language of Predicate Logic

Definition
There are a lot of different formal systems expressing predicate 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 $\mathcal L_1$ to represent the formal language of predicate logic in what follows. In order to define $\mathcal L_1$, 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 $\mathcal L_1$)

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

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

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

Similarly, it is becoming increasingly common to make $=$ part of the signs.

At we aim to incorporate all these different approaches, and thus we have come to separately define the formal language.

For the sakes of modularity and universality, we have settled for the formal language on this page as the language of choice on.

The page Definition:Translation Scheme for Predicate Logic documents how various other approaches from the literature can be translated into ours.

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