Homogeneity and universal quantification in embedded ... - OSF

Homogeneity and universal quantification in embedded questions

Homogeneity and universal quantificationin embedded questions

Dominique Blok and Jordan CharkUniversity of Potsdam // Xprag.de ”ExQ” Project

”Exhaustivity in embedded questions”

Sinn und Bedeutung 25, September 2020

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Universal quantifiers in embedded questions


In Dutch, Ulster English, and German, universal quantifierscan be used in questions as well as embedded questions:

(1) Who all saw a snake?

(2) Joanne knows who all saw a snake.

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Two properties

These expressions have two interesting properties:

1 There is disagreement in the literature on German about theat-issueness of universal quantifiers in embedded questions

2 They have been said to function as homogeneity removers

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1. At-issueness

Disagreement about whether the German universal quantifieralles can be made at-issue in embedded questions:

Reis (1992): alles cannot be focussed or made at-issue

Beck and Rullmann (1999) provide an account of alles as anovert truth-functional instantiation of their answer1 operator(it takes a Hamblin style question denotation as input andyields the maximally informative singleton set, yielding aweakly exhaustive reading), so: it is part of the at-issuecontent

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1. At-issueness

Prediction: if alles is at-issue, negation should be able totarget it:

(3) #DavidDavid

weißknows

nicht,not,

werwho

Reisrice

gegesseneaten

hat.has.

ErHe

weißknows

aber,though,

dassthat

SonjaSonja

Reisrice

gegesseneaten

hat.has.

# ‘David does not know who ate rice. He does knowthat Sonja ate rice though.’

(4) DavidDavid

weißknows

nicht,not,

werwho

allesalles

Reisrice

gegesseneaten

hat.has.

ErHe

weißknows

aber,though,

dassthat

SonjaSonja

Reisrice

gegesseneaten

hat.has.

‘David does not know who all ate rice. He does knowthat Sonja ate rice, though.’

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2. Homogeneity

Kriz (2015): Universal quantifiers in embedded questions are‘homogeneity removers’

Meaning of an embedded question without a universalquantifier:

(5) Agatha knows who came.

(6) true in w iff in all of Agatha’s belief worlds, all thepeople who came in w camefalse in w iff in at least one of Agatha’s belief worlds,none of the people who came in w cameundefined otherwise

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2. Homogeneity

The meaning of an embedded question with a universalquantifier:

(7) Agatha knows who all came.

(8) true in w iff in all of Agatha’s belief worlds, all thepeople who came in w camefalse in w iff in at least one of Agatha’s belief worlds,at least one of the people who came in w didn’t comeundefined never

So: if there are people who came but Agatha does not knowthat they came, this leads to undefinedness without all and tofalsehood with all

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2. Homogeneity

Put differently: universal quantifiers in embedded questionsenforce exhaustive readings

(9) Context: Julia knows that Lisa Bylinina and AnaArregui are invited speakers at SuB. She does notknow about Clemens Steiner-Mayr.

#Julia knows who all are the invited speakers at SuB.

BUT: the predicate know usually gives rise to exhaustivereadings anyway. That’s one of the reasons why we alsolooked at two other different question-embedding predicates

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Question-embedding predicates


1 Universal quantifiers in embedded questions

2 Question-embedding predicates

3 Experimental set-up

4 ResultsDutchEnglishGerman

5 Discussion

6 Analysis - modifier or GQ?

7 Conclusion

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Three predicates

The three predicates we tested in our experiment:

KnowForgetSurprise

We chose these predicates because they differ in theirmonotonicity and distributivity properties

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Know

Know is upward entailing and distributive

Prediction: (10) is better than (11)

(10) Lea does not know who all baked bread, but sheknows that Sebastian baked bread.

(11) Lea does not know who baked bread, but she knowsthat Sebastian baked bread.

If this prediction is borne out, it means that:

All is targeted by negation and therefore part of the at-issuecontent of the sentenceThe presence of all gives rise to exhaustive readings

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Forget

Forget is downward entailing and distributive

Prediction: (12) is better than (13)

(12) Ginny forgot who all fought in the battle, but she didnot forget that Hermione fought in the battle.

(13) Ginny forgot who fought in the battle, but she didnot forget that Hermione fought in the battle.

If this prediction is borne out, it means that:

All is targeted by negation and therefore part of the at-issuecontent of the sentenceThe presence of all gives rise to exhaustive readings

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Surprise

Surprise is non-upward entailing (Cremers, 2016)

Surprise has been argued to be non-distributive (e.g. Lahiri,2002):

(14) Christian was surprised that Marius and Lily madetheir own clothes.6→ Christian was surprised that Marius made his ownclothes.6→ Christian was surprised that Lily made her ownclothes.

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Surprise

Prediction 1, based on introspective judgments: (15) is betterthan (16)

(15) Christian was surprised at who all made their ownclothes, but he was not surprised that Marius madehis own clothes.

(16) Christian was surprised at who made their ownclothes, but he was not surprised that Marius madehis own clothes.

However, if surprise is non-distributive, then even if Christianis surprised about only one person who made their ownclothes, Christian was surprised at who made their ownclothes is true. Therefore, the negated second clause shouldbe fine in both cases

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Surprise

Prediction 2: (17) is better than (18):

(17) Christian was not surprised at who all made their ownclothes, but he was surprised that Marius made hisown clothes.

(18) Christian was not surprised at who made their ownclothes, but he was surprised that Marius made hisown clothes.

This is because in (18), you negate that Christian wassurprised about one or more people who made their ownclothes, which contradicts the second clause

In (17), you merely negate that Christian was surprised aboutall people who made their own clothes, which is compatiblewith the second clause

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Experimental set-up

Experimental set-up





5 Discussion


7 Conclusion

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Experimental set-up

Design

2x2x3:

All: [+-all]Negation: [negation in 1st clause, negation in 2nd clause]Predicate: [know, forget, surprise]

Forced choice: Does the sentence make sense? — Yes/No

16 items per predicate, so 3x16=48 test items

1:1 filler ratio (48+48=96 items in total). Fillers werecounterbalanced with good/bad sentences which couldadditionally be used as baselines for at-issue contradictions

Items presented without a context

Latin square design

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Experimental set-up

Predictions: know

(19) [+all,neg1,know] Lea does not know who all baked bread,but she knows that Sebastian baked bread.

(20) [-all,neg1,know] #Lea does not know who baked bread,but she knows that Sebastian baked bread.

(20) is contradictory because the second clause contradicts thehomogeneity/exhaustivity of the first. (19) is not because allfunctions as a homogeneity remover.

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Experimental set-up

Predictions: forget

(21) [+all,neg2,forget] Ginny forgot who all fought in thebattle, but she did not forget that Hermione fought in thebattle.

(22) [-all,neg2,forget] #Ginny forgot who fought in the battle,but she did not forget that Hermione fought in the battle.

(22) is contradictory because the second clause contradicts thehomogeneity/exhaustivity of the first. (21) is not because allfunctions as a homogeneity remover.

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Experimental set-up

Predictions: surprise

(23) [+all, neg1, surprise] Christian was not surprised at whoall made their own clothes, but he was surprised thatMarius made his own clothes.

(24) [-all, neg1, surprise] #Christian was not surprised at whomade their own clothes, but he was surprised that Mariusmade his own clothes.

(25) [+all, neg2, surprise] Christian was surprised at who allmade their own clothes, but he was not surprised thatMarius made his own clothes.

(26) [-all, neg2, surprise] #Christian was surprised at whomade their own clothes, but he was not surprised thatMarius made his own clothes.

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Results

Results





5 Discussion


7 Conclusion

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Results

Dutch

Results: Dutch

Figure 1: Results for Dutch know,

forget, and surprise

(a) Know (b) Forget

(c) Surprise22 / 52


Results

Dutch

Results: Dutch

For know, forget, and surprise there was a main effect for [+/-all] (p<.001) and for [NEG1/NEG2] (p<.001). For know andforget there was also a significant interaction (p<.001 forknow, p=0.0180 for forget). For surprise there was nointeraction (p=0.917).

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Results

English

Results: English

Figure 2: Results for German know,


a. [+all ]/[Neg1] b. [+all ]/[Neg2]c. [−all ]/[Neg1] d. [−all ]/[Neg2]

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Results

English

Results: English

Figure 2: Results for English know,


a. [+all ]/[Neg1] b. [+all ]/[Neg2]c. [−all ]/[Neg1] d. [−all ]/[Neg2]

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Results

English

Results: English

For know, forget, and surprise there was a main effect for[+/- all] (p<.001). There was also a main effect for[NEG1/NEG2] (p¡.001 for know and forget, p<0.01 forsurprise). For know and forget there was also a significantinteraction (p<.001 for know, p=0.045 for forget). Forsurprise there was no interaction (p=0.47).

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Results

German

Results: German

Figure 2: Results for German know,


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Results

German

Results: German

Figure 2: Results for English know,


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Results

German

Results: German

For know, forget, and surprise there was a main effect for[+/- all] (p<.001) and for [NEG1/NEG2] (p<.001). For knowand forget there was also a significant interaction (p<.001 forknow, p=0.002 for forget). For surprise there was nointeraction (p=0.44).

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Discussion

Discussion





5 Discussion


7 Conclusion

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Discussion

Discussion

Main predictions verified: w-alles is visible to negation in allthree languages. Response patterns are comparable acrossthem and in line with our predictions.

Observation 1: Both [+alles] conditions under surprise wererated quite good; no homogeneity to begin with so the effectof alles is to bias towards the group-composition reading

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Discussion

Discussion

Observation 2: surprise is not as degraded as forget in the[−alles] conditions despite both typically considered to bedownward entailing; may be accounted for in light ofdifferences in distributivity

Observation 3: The (d) condition for surprise received ahigher proportion of felicitous ratings than the (c) condition;(i) surprise under the scope of negation is true iff no p wasunexpected resulting in homogeneity whereas (ii) withoutnegation, Joe is surprised who left is true iff in all doxasticallyaccessible worlds w’ compatible with past expectations thereexists one or more p such that p is false in w’ (=p isunexpected)

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Discussion

Discussion - Homogeneity removal

The second primary claim of our paper is that all functions asa homogeneity remover.

Homogeneity is tied to plural predication in general (Lobner,2000). Homogeneity removal arises where we have universalquantification over atoms, as opposed to plural predication(Kriz, 2015).

→ More generally homogeneity follows because of a relationbetween two arguments of type e. (Cremers, 2018)

How can we model this mechanism?

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Discussion

Discussion - Analysis

There are two analytical possibilities for all : (i) all combineswith a plural individual and outputs a generalized quantifier,or (ii) it is a function from a predicate of individuals to apredicate of individuals (it is a cross-categorical modifier)(Fox, 2018)

J wer-alles K forms a constituent with the wh-word or traceand contributes at-issue proposition-internal maximality.

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Discussion


Alles quantifies directly over the wh-operator (it binds anindefinite-like variable), whereas declined alle is apropositional operator and instead quantifies over therestrictor NP. (Doliana, 2019; Zimmermann, 2008a)

Wessen Munzen sind alle auf Kopf gelandet? → Whose coinsall landed on heads?

Wessen Munzen sind alles auf Kopf gelandet? → What areall the people for which (some) coins landed on heads?

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Discussion

Discussion - ANS

Most accounts of embedded questions encode maximality intothe denotation of the answerhood operator, which functionsas the interface between the embedder and the Hamblin setdenoted by the wh-clause (Dayal, 1981; Fox, 2018; Cremers,2018)

For instance, Cremers (2018:08):

(27) [[ ANS s ]] = ια[Q (α) ∧ ∀β ∈ C → C(Q(α) ⊆Q(β )]]

(28) ANS(Q)(C) = ιp.[Q(p) ∧ C(p) ∧ ∀p′, Q(p’) ∧ C(p’)→ p ⊆ p’] (where C is the embedding restrictor) ≈the true maximal proposition in C

The question remains: If alles contributes at-issue maximality,what happens with this layered maximality?

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Discussion

Discussion - ANS

ANS - w-all (bare): Plural individual exhibitinghomogeneity, cumulativity, quantificational variability

ANS + w-all: Singleton set, no proposition is maximallyinformative (no entailment relations preserved!). Answerpropositions are mutually exclusive (≈ EXH).

all under surprise paves the way for otherwise dispreferred andmore highly marked non-homogenous (non-distributive)readings

Under know, +SE is the preferred interpretation underbare-wh but alles forces a de-dicto construal → x knows thecomplete answer and knows it is the complete answer (dox.available worlds)

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Discussion

Discussion

On the account of Kriz and Spector (2019), plural predicationdenotes candidate interpretations.

A candidate interpretation is ”any disjunctions of themereological parts of the restrictor plurality”, this amounts toall of the possible construals/interpretations, which isequivalent to generalized quantification over individuals.Candidate interpretations are propositions.

All gets co-indexed with the argument position with which itis associated. Syntactic structure feeds the interpretation.With all, scope matters – this is not surprising, as we mayassume that it is a quantifier. We have to capture the factthat homogeneity removal only applies to a local argument.

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Discussion

Discussion

Pieces of the analysis in Kriz and Spector (2019): [[.]] =Interpretation function which is relativised to a model, variableassignment, world(s) and a homogeneity parameter H.

For any value of H, the output is a candidate interpretation.

This parameter takes two arguments: an argument index andan individual. Its output is a generalized quantifier. Thecandidate propositions/interpretations for S(the NPs) where x= sum of all individuals/members in the NP denotation.Candidate denotations are equivalent to Montagovianindividuals of the form λ P.P(x).

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Discussion

Discussion

To put it simply: Candidate interpretations are thosepropositions resulting from abstracting over the world variablew.

In order to do so, we input all possible values for theparameter H. If we assume that the extension of ”girls” isinvariable across worlds and we have 2 girls, {a,b}

a or b or a⊕ba or a⊕bb or a⊕ba⊕b

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Discussion

Discussion

Next, we apply the predicate, i.e. ”eat cake” and we end upwith the equivalent of: λ x. ∀y vA eat’w (y). This predicateapplies to all mereological parts of x. Again, H returns ageneralized quantifier

The predicate combines with the generalized quantifier H(i,⊕girls’w ) which is a disjunction Di ∨ ... ∨ Dn.

The girls ate cake (with the presence of a covert DISToperator): is true iff λ x.∀y vA eat’w(y) is true of at least oneDi and for some Di every atomic part x ∈ Di is in eatw (y).

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Discussion

Discussion

Kriz and Spector (2019) offer the following denotation foradverbial all :

”Let I be a set of indices {i , j ...}; H 'i H’ iff for everyindividual x and every index k not in I, H(x, k) = H(x, k).

J alli P Kw ,H : λ x.∀ H’ 'i H (x) JPKw ,H (x)”

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Discussion

Discussion

Using all makes the choice of a given H irrelevant, aproposition is either true or false for all construals of H in agiven world.

H(i,girls’,w): The set of possible candidate interpretations =(a or b, a or a ⊕ b, b or a ⊕ b, a ⊕ b)

The meaning of J [the girls] [alli dancedi ] K is equal to theconjunction of all propositions resulting from thesecandidates. It is a singleton proposition: a⊕b danced.

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Discussion

Discussion

Under negation, we negate the candidate interpretationsarising from the non-negated predication ≈ ¬(a⊕b danced)

What if all scopes above negation?

LF: [the girls] [alli [t [NOT t dancedi ]]] ∀ H’ 'i H :¬danced’w (H’(i(⊕ girls’w )(a⊕b ¬ danced) = 1 iff neither girl danced, 0 otherwise.

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Analysis - modifier or GQ?


Application to interrogative domain: Boolean join overdisjunctions; along the lines of Zimmermann (2008b)’sanalysis for Hausa wh-based quantifiers.

Wh-expressions range over individuals (Jacobson, 1998;Cooper, 1983)

The (inherent) focus value of a wh-expression denotes a set ofalternatives X (Beck, 2006)

alles combines with an indefinite (locally, at DP level) touniversally quantify over plural individuals, forming a GQ

Application of join at this level results in set union(Zimmermann, 2008b; Szabolcsi, 1997) equivalent touniversal quantification in the domain of individuals

Potential roadblock: alles allows both distributive andcollective interpretations

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Conclusion

Conclusion





5 Discussion


7 Conclusion

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Conclusion

Conclusion

Our data suggest that all must output a single maximalizedproposition. This captures the key difference between w-alland bare wh; the focus denotation in the case of w-all consistsof a singular/unique plural individual (singleton set), in thecase of the latter, the wh-denotation is a plural individual(plurality of propositions).

This fits well conceptually with the view that all is a ”pluralityenforcer” (de Vries, 2019), it constitutes a type-shifter toplural generalized quantifier denotations, serving to ensurethat the predicates in the VP extension only contain the(sum) entity of type e associated with all

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Conclusion

Thank you!This work was funded by the Deutsche Forschungsgemeinschaft(DFG, German Research Foundation), Priority Programme SPP1727 XPRAG.de, Project ’Exhaustivity in embedded questions’.

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Conclusion

Beck, S. (2006). Intervention effects follow from focusinterpretation. Natural Language Semantics, 14, 1-56.

Beck, S., & Rullmann, H. (1999). A flexible approach toexhaustivity in questions. Natural Language Semantics, 7(3),249-298.

Cooper, R. (1983). Quantification and syntactic theory.Dordrecht: Reidel.

Cremers, A. (2016). On the semantics of embedded questions.Ecole Normale Superieure dissertation.

Cremers, A. (2018). Plurality effects in an exhaustification-basedtheory of embedded questions. Nat. Lang. Semantics, 26,193-251.

Dayal, V. (1981). Locality in wh quantification: Questions andrelative clauses in hindi. Kluwer: Dordrecht.

de Vries, H. (2019). Weak all. (Manuscript. Accessed athcommons.org)

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Conclusion

Doliana, A. (2019). Wh-quantifier float in german; new and oldinsights into the theory of quantifier float. UnpublishedManscript, accessed at academia.edu.

Fox, D. (2018). Fox, danny. partition by exhaustification:Comments on dayal 1996. In Proceedings of sinn undbedeutung 22.

Jacobson, P. (1998). On the quantificational force of english freerelatives. In E. B. et al. (Ed.), Quantification in naturallanguages (p. 451-486). Dordrecht: Kluwer.

Kriz, M. (2015). Homogeneity, trivalence, and embeddedquestions. In T. Brochhagen, F. Roelofsen, & N. Theiler(Eds.), Proceedings of the 20th Amsterdam Colloquium.

Kriz, M., & Spector, B. (2019). Interpreting plural predication:Ho- mogeneity and non-maximality. Unpublished Manscript,Lingbuzz; https://ling.auf.net/ lingbuzz/003458.

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Conclusion

Lahiri, U. (2002). Questions and answers in embedded contexts.Oxford: Oxford University Press.

Lobner, S. (2000). Polarity in natural language: Predication,quantification and negation in particular and characterizingsentences. Journal of Semantics, 23, 213-308.

Reis, M. (1992). The category of invariant alles in wh-clauses: onsyntactic quantifiers vs. quantifying particles in German. InR. Tracy (Ed.), Who climbs the grammar-tree (pp.465–492). Niemeyer.

Szabolcsi, A. (1997). Background notions in lattice theory andgeneralized quantifiers. In A. Szabolcsi (Ed.), Ways of scopetaking (p. 179-232). John Benjamins.

Zimmermann, M. (2008a). Quantifying question particles ingerman: Syn- tactic effects on interpretation. In Proceedingsof Sinn & Bedeutung 11.

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Conclusion

Zimmermann, M. (2008b). Variation in the expression of universalquantification and free choice: The case of hausa koo-whexpressions. In Linguistic variation yearbook (p. 179-232).John Benjamins.

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