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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.

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.

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

Trivia

WFF is the basis for an esoteric pun used in the name of a product: "WFF 'n Proof: The Game of Modern Logic," by Layman Allen, a professor at the University of Michigan. The board game is designed to teach the principles of symbolic logic to children (in Polish notation), and its name is a pun on whiffenpoof, a nonsense word used as a cheer at Yale University made popular in The Whiffenpoof Song.

See also

• Formula (mathematical logic)

External links

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

• Logic