Editing Logical disjunction (section)

{{Short description|Logical connective OR}}
{{Redirect|Disjunction|the logic gate|OR gate|separation of chromosomes|Meiosis|disjunctions in distribution|Disjunct distribution}}
{{Redirect|Logical OR|the operator ''‖''|Vertical bars (disambiguation)}}
{{Infobox logical connective
| title        = Logical disjunction
| other titles = OR
| wikifunction = Z10184
| Venn diagram = Venn0111.svg
| definition   = <math>x+y</math>
| truth table  = <math>(1110)</math>
| logic gate   = OR_ANSI.svg
| DNF          = <math>x+y</math>
| CNF          = <math>x+y</math>
| Zhegalkin    = <math>x \oplus y \oplus xy</math>
| 0-preserving = yes
| 1-preserving = yes
| monotone     = yes
| affine       = no
| self-dual    = no
}}
{{Logical connectives sidebar}}
[[File:Venn 0111 1111.svg|thumb|220px|[[Venn diagram]] of <math>\scriptstyle A \lor B \lor C</math>]]

In [[logic]], '''disjunction''' (also known as '''logical disjunction''', '''logical or''', '''logical addition''', or '''inclusive disjunction''') is a [[logical connective]] typically notated as <math> \lor </math> and read aloud as "or". For instance, the [[English language|English]] language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula <math> S \lor W </math>, assuming that <math>S</math> abbreviates "it is sunny" and <math>W</math> abbreviates "it is warm".

In [[classical logic]], disjunction is given a [[truth function]]al semantics according to which a formula <math>\phi \lor \psi</math> is true unless both <math>\phi</math> and <math>\psi</math> are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an ''inclusive'' interpretation of disjunction, in contrast with [[exclusive disjunction]]. Classical [[proof theory|proof theoretical]] treatments are often given in terms of rules such as [[disjunction introduction]] and [[disjunction elimination]]. Disjunction has also been given numerous [[nonclassical logic|non-classical]] treatments, motivated by problems including [[Aristotle's sea battle argument]], [[Heisenberg]]'s [[uncertainty principle]], as well as the numerous mismatches between classical disjunction and its nearest equivalents in [[natural language]]s.<ref name=":1">{{Citation|last=Aloni|first=Maria|author-link=Maria Aloni|title=Disjunction|date=2016|url=https://plato.stanford.edu/archives/win2016/entries/disjunction/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2016|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-09-03}}</ref><ref>{{Cite web|title=Disjunction {{!}} logic|url=https://www.britannica.com/topic/disjunction-logic|access-date=2020-09-03|website=Encyclopedia Britannica|language=en}}</ref>

An [[operand]] of a disjunction is a '''disjunct'''.<ref name=":21">{{Cite book |last=Beall |first=Jeffrey C. |title=Logic: the basics |date=2010 |publisher=Routledge |isbn=978-0-203-85155-5 |edition=1. publ |location=London |pages=57 |language=en}}</ref>