Editing Exclusive or (section)

==Exclusive or in natural language==

Disjunction is often understood exclusively in [[natural language]]s. In English, the disjunctive word "or" is often understood exclusively, particularly when used with the particle "either". The English example below would normally be understood in conversation as implying that Mary is not both a singer and a poet.<ref name= "alonisep">{{cite encyclopedia|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>Jennings quotes numerous authors saying that the word "or" has an exclusive sense. See Chapter 3, "The First Myth of 'Or'":<br />{{cite book |last=Jennings |first=R. E. |date=1994 |title=The Genealogy of Disjunction |location=New York |publisher=Oxford University Press }}</ref>

:1. Mary is a singer or a poet.

However, disjunction can also be understood inclusively, even in combination with "either". For instance, the first example below shows that "either" can be [[felicity (pragmatics)|felicitously]] used in combination with an outright statement that both disjuncts are true. The second example shows that the exclusive inference vanishes away under [[downward entailing]] contexts. If disjunction were understood as exclusive in this example, it would leave open the possibility that some people ate both rice and beans.<ref name= "alonisep"/>

:2. Mary is either a singer or a poet or both.
:3. Nobody ate either rice or beans.

Examples such as the above have motivated analyses of the exclusivity inference as [[pragmatics|pragmatic]] [[conversational implicature]]s calculated on the basis of an inclusive [[formal semantics (linguistics)|semantics]]. Implicatures are typically [[cancellable (linguistics)|cancellable]] and do not arise in downward entailing contexts if their calculation depends on the [[Cooperative_principle#Maxim of quantity (content length and depth)|Maxim of Quantity]]. However, some researchers have treated exclusivity as a bona fide semantic [[entailment]] and proposed nonclassical logics which would validate it.<ref name= "alonisep" />

This behavior of English "or" is also found in other languages. However, many languages have disjunctive constructions which are robustly exclusive such as French ''soit... soit''.<ref name= "alonisep" />