A formal language is a structure $\mathcal L$ which comprises:
- A set of symbols $\mathcal A$ called the alphabet of $\mathcal L$
- A collation system with the unique readability property for $\mathcal A$
- A formal grammar that determines which collations belong to the formal language and which do not.
Let $\mathcal L$ be a formal language.
An alphabet consists of the following parts:
Depending on the specific nature of any particular formal language, these too may be subcategorized.
Common examples of signs are parentheses, "(" and ")", and the comma, ",".
The logical connectives are also signs.
A key feature of collations is the presence of methods to collate a number of collations into a new one.
A collection of collations, together with a collection of such collation methods may be called a collation system.
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): $\S 2.1$: Introduction
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $1$: Introduction: $\S 1.2$: Propositional and predicate calculus
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (next): $\S 1$: Propositional Logic
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: language