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In logic, WFF (pronounced "wiff") is an abbreviation for well-formed formula. Given a formal grammar, a WFF is any string that is generated by that grammar.

In formal logic, proofs are sequences of WFFs with certain properties, and the final WFF in the sequence is what is proven.

Examples

For example, in propositional logic the sequence of symbols

${\displaystyle ((\alpha \rightarrow \beta )\rightarrow (\neg \beta \rightarrow \neg \alpha ))}$

is a WFF because it is grammatically correct. The sequence of symbols

${\displaystyle ((\alpha \rightarrow \beta )\rightarrow (\beta \beta ))\alpha ))}$

is not a WFF, because it does not conform to the grammar of propositional calculus.

Trivia

WFF is the basis for an esoteric pun used in the name of a game product: "WFF 'N PROOF: The Game of Modern Logic," by Layman Allen, developed while he was at Yale Law School (he was later a professor at the University of Michigan). The suite of games is designed to teach the principles of symbolic logic to children (in Polish notation). Its name is an accepted pun on whiffenpoof, a nonsense word used as a cheer at Yale University made popular in The Whiffenpoof Song and The Whiffenpoofs.

Notes

2. More technically, propositional logic using the Fitch-style calculus.

See also

• Formula (mathematical logic)
• Woodhull Freedom Foundation & Federation (acronym WFF)

External links

• Well-Formed Formula for First Order Predicate Logic - includes a short Java quiz.
• Well-Formed Formula at ProvenMath

• Logic