Editing Logical connective (section)

==Order of precedence==
As a way of reducing the number of necessary parentheses, one may introduce [[precedence rule]]s: &not; has higher precedence than &and;, &and; higher than &or;, and &or; higher than →. So for example, <math>P \vee Q \and{\neg R} \rightarrow S</math> is short for <math>(P \vee (Q \and (\neg R))) \rightarrow S</math>.

Here is a table that shows a commonly used precedence of logical operators.<ref>{{cite book|title=Discrete Mathematics Using a Computer|first1=John|last1=O'Donnell|first2=Cordelia|last2=Hall|first3=Rex|last3=Page| publisher=Springer| year=2007| isbn=9781846285981|page=120|url=https://books.google.com/books?id=KKxyQQWQam4C&pg=PA120}}.</ref><ref name=":35">{{Cite book |last1=Allen |first1=Colin |title=Logic primer |last2=Hand |first2=Michael |date=2022 |publisher=The MIT Press |isbn=978-0-262-54364-4 |edition=3rd |location=Cambridge, Massachusetts}}</ref>
{| class="wikitable" style="text-align: center;"
!Operator !!Precedence
|-
| <math>\neg</math> || 1
|-
| <math>\and</math> || 2
|-
| <math>\vee</math> || 3
|-
| <math>\rightarrow</math> || 4
|-
| <math>\leftrightarrow</math> || 5
|}
However, not all compilers use the same order; for instance, an ordering in which disjunction is lower precedence than implication or bi-implication has also been used.<ref>{{cite book|title=Software Abstractions: Logic, Language, and Analysis | first=Daniel|last=Jackson|publisher=MIT Press|year=2012|isbn=9780262017152|page=263| url=https://books.google.com/books?id=DDv8Ie_jBUQC&pg=PA263}}.</ref> Sometimes precedence between conjunction and disjunction is unspecified requiring to provide it explicitly in given formula with parentheses. The order of precedence determines which connective is the "main connective" when interpreting a non-atomic formula.