# Definition:Rule of Formation

## Definition

Let $\FF$ be a formal language whose alphabet is $\AA$.

The **rules of formation** of $\FF$ are the rules which define how to construct collations in $\AA$ which are well-formed.

That is, the **rules of formation** tell you how to build collations featuring symbols from the alphabet $\AA$ which are part of the formal language $\FF$.

The **rules of formation** of a formal language together constitute its formal grammar.

There are no strict guidelines on what a **rule of formation** should look like, since they are employed to *produce* such strict guidelines.

Thus, these **rules of formation** are often phrased in natural language, and their exact form is to some extent arbitrary.

## Examples

### Not A

In the language of propositional logic, logical negation is implemented using the **rule of formation**:

## Also known as

**Rules of formation** are also referred to in some sources as **rules of syntax**.

Some sources prefer the construct **formation rules**.

## Also see

- Definition:BNF Specification of Propositional Logic, in which one can see
**rules of formation**employed. - Definition:Bottom-Up Specification of Propositional Logic, a different approach to
**rules of formation**.

- Results about
**rules of formation**can be found**here**.

## Sources

- 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (previous) ... (next): $\S 4.2$: The Construction of an Axiom System - 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $1$ Formation Rules - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.2$: Syntax of Propositional Logic - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**formal language** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**formation rules** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**formal language** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**formation rules**