# Definition:Well-Formed Formula

## Definition

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

A **well-formed formula** is a collation in $\mathcal A$ which can be built by using the rules of formation of the formal grammar of $\mathcal F$.

That is, a collation in $\mathcal A$ is a **well-formed formula** in $\mathcal F$ if and only if it has a parsing sequence in $\mathcal F$.

## Also known as

This is often encountered in its abbreviated form **WFF**, pronounced something like **woof** or **oof**, depending on personal preference.

Alternative names include **well-formed word** or simply **formula**.

**(Well-formed) expression** is also seen.

## Sources

- 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (previous) ... (next): $\S 4.1$: The Purpose of the Axiomatic Method - 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): $\S 2.1$: Formation Rules (in the context of the language of propositional logic) - 1993: M. Ben-Ari:
*Mathematical Logic for Computer Science*(1st ed.) ... (previous) ... (next): $\S 2.2$: Propositional formulas - 2000: Michael R.A. Huth and Mark D. Ryan:
*Logic in Computer Science: Modelling and reasoning about systems*... (previous) ... (next): $\S 1.3$: Propositional logic as a formal language - 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (previous) ... (next): $\S 2.1$