# Definition:Rule of Formation

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## Definition

Let $\mathcal F$ be a formal language whose alphabet is $\mathcal A$.

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

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

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

There are no strict guidelines on how 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, but their exact form is to some extent arbitrary.

## Also known as

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

## 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**.

## 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): $\S 2.1$: Formation Rules - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.2$: Syntax of Propositional Logic