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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'''. That is, given a ] to produce strings, the assertion 'string ''S'' is a WFF' only means that it really is produced by the ].


For example, in ] the sequence of symbols <math>((\alpha\rightarrow\beta)\rightarrow(\neg\beta\rightarrow\neg\alpha))</math> is a wff because it is gramatically 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 (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.


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


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Revision as of 01:07, 28 December 2003

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 ( ( α → β ) → ( ¬ β → ¬ α ) ) {\displaystyle ((\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 ( ( 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.

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.

External link