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:

(1)	a.	Some student attended the class yesterday.
	b.	Every student attended the class yesterday.

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):

(2)	Truth conditions:
	a.	$[[some\ student\ attended\ the\ class\ yesterday]]$	$=$	$True$	if: at least one of $\{alice,bertrand,clarice\}$ is in the set of students who attended the class yesterday.
			$=$	$False$	if: none of $\{alice,bertrand,clarice\}$ is in the set of students who attended the class yesterday.
	b.	$[[every\ student\ attended\ the\ class\ yesterday]]$	$=$	$True$	if: all of $\{alice,bertrand,clarice\}$ are in the set of students who attended the class yesterday.
			$=$	$False$	otherwise.

in which a disjunction like or (1)

(1)	Xavier or Yvette arrived.
	i.	Truth conditions, where

Examples of exhaustivity

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.

(1)	Xavier taught linguistics to Yvette or Zach.
	a.	Xavier taught linguistics to Yvette, but not Zach.
	b.	Xavier taught linguistics to Zach, but not Yvette.
	c.	Xavier taught linguistics to Zach and Yvette.

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

$p$	$q$	$p\lor q$
T	T	T
T	F	T
F	T	T
F	F	F

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:

  $exh(ALT,\phi )=\phi \wedge V\{\neg a:\ a\in ALT\wedge \phi \ does\ not\ entail\ a\}$

See also

• Alternative semantics
• Focus
• Paul Grice

Bibliography

• Chierchia, Gennaro (2004). "Scalar implicature, polarity phenomena, and the syntax/pragmatics interface". In Belleti, Adriana (ed.). Structures and Beyond. Oxford University Press. pp. 39–103.
• Chierchia, Gennaro (2013). Logic in grammar: Polarity, Free choice, and Intervention. Oxford University Press.
• Chierchia, Gennaro; Fox, Danny; Spector, Benjamin (2012). "Scalar implicature as a grammatical phenomenon". In von Heusinger, Klaus; Maienborn, Claudia; Portner, Paul (eds.). Handbook of semantics. Vol. 3. Mouten de Gruyter. pp. 2297–2331. Archived from the original on April 5, 2022.
• Fox, Danny (2007). "Free choice and the theory of scalar implicatures". In Sauerland, Uli; Stateva, Penka (eds.). Presupposition and implicature in compositional semantics. New York: Palgrave Macmillan. pp. 537–586. doi:10.1093/jos/10.4.269.
• Grice, H.P. (1975). "Logic and Conversation". In Cole, P.; Morgan, J. (eds.). Syntax and Semantics. Vol. 3.
• Karttunen, L.; Peters, S. (1979). "Conventional implicature". In Oh, C.-K.; Dinneen, D. A. (eds.). Presupposition. New York: Academic Press.
• Krifka, Manfred (1993). "Focus and presupposition in dynamic interpretation". Journal of Semantics. Vol. 10, no. 4. pp. 269–300. doi:10.1093/jos/10.4.269.
• Krifka, Manfred (1995). "The semantics and pragmatics of polarity items". Linguistic Analysis. Vol. 24. pp. 209=257.
• Rooth, Mats (1992). "A theory of focus interpretation". Natural Language Semantics. Vol. 1, no. 1. pp. 75–116.
• Rooth, Mats (2016). "Alternative semantics". In Féry, Caroline; Ishihara, Shinichiro (eds.). The Oxford Handbook of Information Structure. Oxford University Press. doi:10.1093/oxfordhb/9780199642670.013.19.
• Spector, Benjamin (2016). "Comparing exhaustivity operators". Semantics and Pragmatics. 9 (11): 1–13. doi:10.3765/sp.9.11.