# Definition:Well-Formed Formula

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## Definition

Let $\FF$ be a formal language whose alphabet is $\AA$.

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

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

## Also known as

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

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

Some less formal approaches use the term **statement form**.

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

## Also see

## 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*... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.2$: 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 - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**well-formed formula** - 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (previous) ... (next): $\S 2.1$