Editing Propositional formula (section)

{{Short description|Logic formula}}

In [[propositional logic]], a '''propositional formula''' is a type of syntactic [[Formula (mathematical logic)|formula]] which is [[well formed formula|well formed]]. If the values of all variables in a propositional formula are given, it determines a unique [[truth value]]. A propositional formula may also be called a '''propositional expression''', a '''sentence''',<ref>{{cite book|chapter-url=http://intrologic.stanford.edu/chapters/chapter_02.html |title=Introduction to Logic |isbn=9783031018015 |edition=3rd |doi=10.1007/978-3-031-01801-5 |author-last2=Genesereth |author-first2=Michael |author-first1=Eric J. |author-last1=Kao |year=2017 |chapter=Propositional Logic|series=Synthesis Lectures on Computer Science }}</ref> or a '''sentential formula'''.

A propositional formula is constructed from simple [[Proposition (logic)|proposition]]s, such as "five is greater than three" or [[propositional variable]]s such as ''p'' and ''q'', using connectives or [[logical operator]]s such as NOT, AND, OR, or IMPLIES; for example:

: (''p'' AND NOT ''q'') IMPLIES (''p'' OR ''q'').

In [[mathematics]], a propositional formula is often more briefly referred to as a "'''proposition'''", but, more precisely, a propositional formula is not a proposition but a [[formal expression]] that ''denotes'' a [[Proposition (mathematics)|proposition]], a [[formal object]] under discussion, just like an expression such as "{{nowrap|''x'' + ''y''}}" is not a value, but denotes a value. In some contexts, maintaining the distinction may be of importance.