Editing Well-formed formula (section)

{{Short description|Syntactically correct logical formula}}
{{broader|Mathematical formula}}
{{Formal languages}}

In [[mathematical logic]], [[propositional logic]] and [[predicate logic]], a '''well-formed formula''', abbreviated '''WFF''' or '''wff''', often simply '''formula''', is a finite [[sequence]] of [[symbol (formal)|symbols]] from a given [[alphabet (computer science)|alphabet]] that is part of a [[formal language]].<ref>Formulas are a standard topic in introductory logic, and are covered by all introductory textbooks, including Enderton (2001), Gamut (1990), and Kleene (1967)</ref>

The abbreviation '''wff''' is pronounced "woof", or sometimes "wiff", "weff", or "whiff".{{refn|
* "woof"<ref>{{Cite book |last=Gensler |first=Harry |url=https://books.google.com/books?id=YjuCAgAAQBAJ |title=Introduction to Logic |date=2002-09-11 |publisher=Routledge |isbn=978-1-134-58880-0 |pages=35 |language=en}}</ref><ref>{{Cite book |last1=Hall |first1=Cordelia |url=https://books.google.com/books?id=QZgKCAAAQBAJ |title=Discrete Mathematics Using a Computer |last2=O'Donnell |first2=John |date=2013-04-17 |publisher=Springer Science & Business Media |isbn=978-1-4471-3657-6 |pages=44 |language=en}}</ref><ref>{{Cite book |last=Agler |first=David W. |url=https://books.google.com/books?id=nhQHlwV5NSIC |title=Symbolic Logic: Syntax, Semantics, and Proof |date=2013 |publisher=Rowman & Littlefield |isbn=978-1-4422-1742-3 |pages=41 |language=en}}</ref><ref>{{Cite book |last=Simpson |first=R. L. |url=https://books.google.com/books?id=w2doAwAAQBAJ |title=Essentials of Symbolic Logic - Third Edition |date=2008-03-17 |publisher=Broadview Press |isbn=978-1-77048-495-5 |pages=14 |language=en}}</ref> 
* "wiff"<ref>{{Cite book |last=Laderoute |first=Karl |title=A Pocket Guide to Formal Logic |date=2022-10-24 |publisher=Broadview Press |isbn=978-1-77048-868-7 |pages=59 |language=en}}</ref><ref>{{Cite book |last1=Maurer |first1=Stephen B. |url=https://books.google.com/books?id=SWds5v8UUc4C |title=Discrete Algorithmic Mathematics, Third Edition |last2=Ralston |first2=Anthony |date=2005-01-21 |publisher=CRC Press |isbn=978-1-56881-166-6 |pages=625 |language=en}}</ref><ref>{{Cite book |last=Martin |first=Robert M. |url=https://books.google.com/books?id=0sOpx5-90d4C |title=The Philosopher's Dictionary - Third Edition |date=2002-05-06 |publisher=Broadview Press |isbn=978-1-77048-215-9 |pages=323 |language=en}}</ref>
* "weff"<ref>{{Cite book |last=Date |first=Christopher |url=https://books.google.com/books?id=HMIay77Pkv0C |title=The Relational Database Dictionary, Extended Edition |date=2008-10-14 |publisher=Apress |isbn=978-1-4302-1042-9 |pages=211 |language=en}}</ref><ref>{{Cite book |last=Date |first=C. J. |url=https://books.google.com/books?id=TB5UCwAAQBAJ |title=The New Relational Database Dictionary: Terms, Concepts, and Examples |date=2015-12-21 |publisher="O'Reilly Media, Inc." |isbn=978-1-4919-5171-2 |pages=241 |language=en}}</ref>
* "whiff"<ref>{{Cite book |last=Simpson |first=R. L. |url=https://books.google.com/books?id=exeO4UNCJ8cC |title=Essentials of Symbolic Logic |date=1998-12-10 |publisher=Broadview Press |isbn=978-1-55111-250-3 |pages=12 |language=en}}</ref> 
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".}}

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