Definition:Well-Formed Formula

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

The term well-formed formula is often encountered in its abbreviated form WFF or 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

• Definition:WFF of Propositional Logic
• Definition:WFF of Predicate Logic

• Results about well-formed formulas can be found here.

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): Chapter $2$: The Propositional Calculus $2$: $1$ 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
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): well-formed formula (wff)
• 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): well-formed formula (wff)
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.1$
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): well-formed formula (wff)