# Definition:Language of Predicate Logic/Bourbaki

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## Definition

There are many formal languages expressing predicate logic.

The formal language used on $\mathsf{Pr} \infty \mathsf{fWiki}$ is defined on Definition:Language of Predicate Logic.

This page defines the formal language $\LL_1$ used in:

- 1968: Nicolas Bourbaki:
*Theory of Sets*

Explanations are omitted as this is intended for reference use only.

### Alphabet

#### Letters

The letters used comprise two classes:

- First, a class of variables $A, A', A
*, \ldots$, called "letters"* - Second, a signature, called the "specific signs"
- The relation symbols are called "relational signs"
- The function symbols are called "substantific signs"

See the $\mathsf{Pr} \infty \mathsf{fWiki}$ definition.

#### Signs

The signs used are the following:

\(\ds \lor \) | \(\ds : \) | the disjunction sign | |||||||

\(\ds \neg \) | \(\ds : \) | the negation sign | |||||||

\(\ds \Box \) | \(\ds : \) | signifying a quantified variable | |||||||

\(\ds \tau \) | \(\ds : \) | signifying an existential quantifier |

and are called "logical signs".

See the $\mathsf{Pr} \infty \mathsf{fWiki}$ definition.

### Collation System

The collation system used is that of Bourbaki assemblies.

See the $\mathsf{Pr} \infty \mathsf{fWiki}$ definition.

### Formal Grammar

This needs considerable tedious hard slog to complete it.In particular: This mess is spread around the first sectionsTo discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Finish}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Also see

## Sources

This needs considerable tedious hard slog to complete it.In particular: Someone who wants to bother could split this page in subpages and have specific source flow. #NotItTo discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Finish}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

- 1968: Nicolas Bourbaki:
*Theory of Sets*... (previous) ... (next): Chapter $\text I$: Description of Formal Mathematics: $1$. Terms and Relations: $1$. Signs and Assemblies*(defining logical signs)* - 1968: Nicolas Bourbaki:
*Theory of Sets*... (previous) ... (next): Chapter $\text I$: Description of Formal Mathematics: $1$. Terms and Relations: $1$. Signs and Assemblies*(defining specific signs)*