Definition:Rule of Formation
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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 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.
- 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.
- 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