Editing Logical disjunction (section)

== Natural language ==

Disjunction in [[natural language]]s does not precisely match the interpretation of <math>\lor</math> in classical logic. Notably, classical disjunction is inclusive while natural language disjunction is often understood exclusively, as the following English example typically would be.<ref name=":1" />

:* Mary is eating an apple or a pear.

This inference has sometimes been understood as an [[entailment]], for instance by [[Alfred Tarski]], who suggested that natural language disjunction is [[lexical ambiguity|ambiguous]] between a classical and a nonclassical interpretation. More recent work in [[pragmatics]] has shown that this inference can be derived as a [[conversational implicature]] on the basis of a [[formal semantics (natural language)|semantic]] denotation which behaves classically. However, disjunctive constructions including [[Hungarian language|Hungarian]] ''vagy... vagy'' and [[French language|French]] ''soit... soit'' have been argued to be inherently exclusive, rendering un[[grammaticality]] in contexts where an inclusive reading would otherwise be forced.<ref name=":1" />

Similar deviations from classical logic have been noted in cases such as [[free choice inference|free choice disjunction]] and [[simplification of disjunctive antecedents]], where certain [[linguistic modality|modal operators]] trigger a [[logical conjunction|conjunction]]-like interpretation of disjunction. As with exclusivity, these inferences have been analyzed both as implicatures and as entailments arising from a nonclassical interpretation of disjunction.<ref name=":1" />

:* You can have an apple or a pear.
::<math>\rightsquigarrow</math> You can have an apple and you can have a pear (but you cannot have both)

In many languages, disjunctive expressions play a role in question formation.
:* Is Mary a philosopher or a linguist?
For instance, while the above English example can be interpreted as a [[polar question]] asking whether it's true that Mary is either a philosopher or a linguist, it can also be interpreted as an [[alternative question]] asking which of the two professions is hers. The role of disjunction in these cases has been analyzed using nonclassical logics such as [[alternative semantics]] and [[inquisitive semantics]], which have also been adopted to explain the free choice and simplification inferences.<ref name=":1" />

In English, as in many other languages, disjunction is expressed by a [[coordinating conjunction]]. Other languages express disjunctive meanings in a variety of ways, though it is unknown whether disjunction itself is a [[linguistic universal]]. In many languages such as [[Dyirbal language|Dyirbal]] and [[Maricopa language|Maricopa]], disjunction is marked using a verb [[suffix]]. For instance, in the Maricopa example below, disjunction is marked by the suffix ''šaa''.<ref name=":1" />

{{interlinear|| lang=mrc|indent=3|ablist=INFER:inferential
|Johnš Billš vʔaawuumšaa |
|John-NOM Bill-NOM 3-come-PL-FUT-INFER
|'John or Bill will come.'}}