Well-formed formula

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.^[1]

The abbreviation wff is pronounced "woof",^[2]^[3]^[4]^[5] or sometimes^[6] "wiff",^[7]^[8]^[9], "weff",^[10]^[11] or "whiff".^[12]

A formal language can be identified with the set of formulas in the language. A formula is a syntactic object that can be given a semantic meaning by means of an interpretation. Two key uses of formulas are in propositional logic and predicate logic.

^ Formulas are a standard topic in introductory logic, and are covered by all introductory textbooks, including Enderton (2001), Gamut (1990), and Kleene (1967)
^ Gensler, Harry (2002-09-11). Introduction to Logic. Routledge. p. 35. ISBN 978-1-134-58880-0.
^ Hall, Cordelia; O'Donnell, John (2013-04-17). Discrete Mathematics Using a Computer. Springer Science & Business Media. p. 44. ISBN 978-1-4471-3657-6.
^ Agler, David W. (2013). Symbolic Logic: Syntax, Semantics, and Proof. Rowman & Littlefield. p. 41. ISBN 978-1-4422-1742-3.
^ Simpson, R. L. (2008-03-17). Essentials of Symbolic Logic - Third Edition. Broadview Press. p. 14. ISBN 978-1-77048-495-5.
^ All sources supported "woof". The sources cited for "wiff", "weff", and "whiff" gave these pronunciations as alternatives to "woof". The Gensler source gives "wood" and "woofer" as examples of how to pronounce the vowel in "woof".
^ Laderoute, Karl (2022-10-24). A Pocket Guide to Formal Logic. Broadview Press. p. 59. ISBN 978-1-77048-868-7.
^ Maurer, Stephen B.; Ralston, Anthony (2005-01-21). Discrete Algorithmic Mathematics, Third Edition. CRC Press. p. 625. ISBN 978-1-56881-166-6.
^ Martin, Robert M. (2002-05-06). The Philosopher's Dictionary - Third Edition. Broadview Press. p. 323. ISBN 978-1-77048-215-9.
^ Date, Christopher (2008-10-14). The Relational Database Dictionary, Extended Edition. Apress. p. 211. ISBN 978-1-4302-1042-9.
^ Date, C. J. (2015-12-21). The New Relational Database Dictionary: Terms, Concepts, and Examples. "O'Reilly Media, Inc.". p. 241. ISBN 978-1-4919-5171-2.
^ Simpson, R. L. (1998-12-10). Essentials of Symbolic Logic. Broadview Press. p. 12. ISBN 978-1-55111-250-3.

[1] Formulas are a standard topic in introductory logic, and are covered by all introductory textbooks, including Enderton (2001), Gamut (1990), and Kleene (1967)

[2] Gensler, Harry (2002-09-11). Introduction to Logic. Routledge. p. 35. ISBN 978-1-134-58880-0.

[3] Hall, Cordelia; O'Donnell, John (2013-04-17). Discrete Mathematics Using a Computer. Springer Science & Business Media. p. 44. ISBN 978-1-4471-3657-6.

[4] Agler, David W. (2013). Symbolic Logic: Syntax, Semantics, and Proof. Rowman & Littlefield. p. 41. ISBN 978-1-4422-1742-3.

[5] Simpson, R. L. (2008-03-17). Essentials of Symbolic Logic - Third Edition. Broadview Press. p. 14. ISBN 978-1-77048-495-5.

[6] All sources supported "woof". The sources cited for "wiff", "weff", and "whiff" gave these pronunciations as alternatives to "woof". The Gensler source gives "wood" and "woofer" as examples of how to pronounce the vowel in "woof".

[7] Laderoute, Karl (2022-10-24). A Pocket Guide to Formal Logic. Broadview Press. p. 59. ISBN 978-1-77048-868-7.

[8] Maurer, Stephen B.; Ralston, Anthony (2005-01-21). Discrete Algorithmic Mathematics, Third Edition. CRC Press. p. 625. ISBN 978-1-56881-166-6.

[9] Martin, Robert M. (2002-05-06). The Philosopher's Dictionary - Third Edition. Broadview Press. p. 323. ISBN 978-1-77048-215-9.

[10] Date, Christopher (2008-10-14). The Relational Database Dictionary, Extended Edition. Apress. p. 211. ISBN 978-1-4302-1042-9.

[11] Date, C. J. (2015-12-21). The New Relational Database Dictionary: Terms, Concepts, and Examples. "O'Reilly Media, Inc.". p. 241. ISBN 978-1-4919-5171-2.

[12] Simpson, R. L. (1998-12-10). Essentials of Symbolic Logic. Broadview Press. p. 12. ISBN 978-1-55111-250-3.

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