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


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


⚫ In formal logic, ]s are sequences of WFFs with certain properties, and the final WFF in the sequence is what is proven. This 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 ]. The board game is designed to teach the principles of symbolic logic to children (in ]), and its name is a pun on ''whiffenpoof'', a nonsense word used as a ] at ] made popular in ''The Whiffenpoof Song''.
Informally, WFFs are the sequences of symbols which have meaning in a given logical system.


⚫ In ], a WFF is often the basis of a ], 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 ]. The board game is designed to teach the principles of symbolic logic to children (in ]), and its name is a pun on ''whiffenpoof'', a nonsense word used as a ] at ] made popular in ''The Whiffenpoof Song''.

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


==External links== ==External links==

Revision as of 02:27, 22 April 2005

In logic, WFF 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 calculus the sequence of symbols ( ( α → β ) → ( ¬ β → ¬ α ) ) {\displaystyle ((\alpha \rightarrow \beta )\rightarrow (\neg \beta \rightarrow \neg \alpha ))} is a WFF because it is grammatically correct. The sequence of symbols ( ( α → β ) → ( β β ) ) α ) ) {\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. This 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.


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