Definition:Language of Predicate Logic/Bourbaki

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

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Also see

• Definition:Language of Predicate Logic

Sources

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• 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)