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# Science Fair Project Encyclopedia

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# WFF

In logic, WFF is an abbreviation for well-formed formula. That is, given a formal grammar to produce strings, the assertion 'string S is a WFF' only means that it really is produced by the grammar.

For example, in propositional calculus the sequence of symbols $((\alpha\rightarrow\beta)\rightarrow(\neg\beta\rightarrow\neg\alpha))$ is a WFF because it is grammatically correct (in fact, it is a tautology). The sequence of symbols $((\alpha\rightarrow\beta)\rightarrow(\beta\beta))\alpha))$ is not a WFF, because it does not conform to the grammar of propositional calculus.

Informally, WFFs are the sequences of symbols which have meaning in a given logical system.

In mathematics, a WFF is often the basis of a proof, which leads to one of the most notoriously esoteric puns ever 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.

Incidentally, "Why is not a WFF." is the correct answer to the often talked about Philosophy exam question "Why?" (as opposed to "Why not?").