User:Biktor627/Exhaustivity

In linguistics exhaustivity refers to an implicature in which a proposition is strengthened by denying its stronger alternatives. It is a major topic in the linguistic subfields of semantics and pragmatics.

The foundational basis of exhaustivity is Gricean informal pragmatics, specifically scalar implicatures in which a existential quantifier like some is strengthened by denying its stronger alternative (e.g. all). Much of the work in the area of exhaustivity can be characterized as giving a formal semantic account of contexts where elements in language are interpreted exhaustively, including focus,, disjunction,, questions,, free choice phenomena,, and polarity items.

Basis of exhaustivity
The empirical and theoretical basis of exhaustivity is Gricean informal pragmatics, in particular contexts where a word or phrase expressing existential quantification like some has stronger alternatives which are reasoned to be false (i.e., denied). That is, the pragmatic meaning of an utterance is stronger than the basic truth conditions. For example, in (1a) some in the noun phrase some student is conventionally implicated to mean not ever student as in (1b) is false:

If there are three contextually relevant students Alice, Bertrand, Clarice, then some student in (1a) has the basic truth conditions as in (2a), while every student (1b) has the truth conditions in (2b):

in which a disjunction like or (1)

Disjunction
For example, in (1), the disjunctive or is true when Xavier taught only Yvette (a), when Xavier taught only Zach (b), or when Xavier taught both Yvette and Zach.

where $$p$$=Xavier taught linguistics to Yvette, $$q$$=Xavier taught linguistics to Zach,

Exhaustivitity operators

 * Krifka
 * $$\lambda w. \phi (w)=1\wedge \forall a((a\in ALT \wedge a(w) =1) \rightarrow (\phi \subseteq a)) $$
 * which is equivalent to:
 * $$exh (ALT,\phi)=\phi \wedge V\{\neg a:\ a\in ALT \wedge \phi\ does\ not\ entail\ a\}$$