# Definition:Language of Propositional Logic/Formal Grammar/WFF

## Definition

Let $\mathbf A$ be approved of by the formal grammar of propositional logic.

Then $\mathbf A$ is called a **well-formed formula of propositional logic**.

Often, one abbreviates "well-formed formula", speaking of a **WFF of propositional logic** instead.

More informally, a **WFF of propositional logic** is any sequence of symbols containing statement variables, such that when statements are substituted for the statement variables (the same statement for any given statement variable throughout), the result is a statement.

## Also known as

There are many ways this concept is addressed in the literature, for instance:

**propositional formula****statement form****logical formula**

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$, logical formula is a term used to refer to *any* kind of expression used in symbolic logic, whereas **statement form** is used in this way in some sources.

Hence on $\mathsf{Pr} \infty \mathsf{fWiki}$ **WFF of propositional logic** and **propositional formula** are the terms of choice for this concept.

## Also see

## Sources

- 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $1$ Formation Rules - 1973: Irving M. Copi:
*Symbolic Logic*(4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.4$: Statement Forms - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.2$: Syntax of Propositional Logic - 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (previous) ... (next): $\S 2.1.6$: Definition $2.13$