Wh-quantification in
Alternative Semantics
Michael Yoshitaka Erlewine (mitcho)
National University of Singapore
mitcho@nus.edu.sg

GLOW in Asia XII / SICOGG XXI
Dongguk University, August 2019

Wh-quantification
We commonly think of question-formation as the primary use ofwh-phrases. But in many languages, wh-phrases are also used forquantification.

(1)

Uses of Japanese dare:(Shimoyama 2006:143)
whda’reinterrogative ‘who’
wh-MO (?) da’re-mo
universal ‘everyone’
wh-DISJ
da’re-ka
existential ‘someone’
wh-EVEN
dare-mo
NPI ‘anyone’
wh-CSP
dare-demo free choice ‘anyone’

Kuroda (1965:43) introduced the term “indeterminate” to refer towh-words as “nouns that behave like a logical variable.”2

Wh-quantification
We commonly think of question-formation as the primary use ofwh-phrases. But in many languages, wh-phrases are also used forquantification.

(1)

Uses of Japanese dare:(Shimoyama 2006:143)
whda’reinterrogative ‘who’
wh-MO (?) da’re-mo
universal ‘everyone’
wh-DISJ
da’re-ka
existential ‘someone’
wh-EVEN
dare-mo
NPI ‘anyone’
wh-CSP
dare-demo free choice ‘anyone’

Kuroda (1965:43) introduced the term “indeterminate” to refer towh-words as “nouns that behave like a logical variable.”2

Wh-quantification
We commonly think of question-formation as the primary use ofwh-phrases. But in many languages, wh-phrases are also used forquantification.

(1)

Uses of Japanese dare:(Shimoyama 2006:143)
whda’reinterrogative ‘who’
wh-MO (?) da’re-mo
universal ‘everyone’
wh-DISJ
da’re-ka
existential ‘someone’
wh-EVEN
dare-mo
NPI ‘anyone’
wh-CSP
dare-demo free choice ‘anyone’

Kuroda (1965:43) introduced the term “indeterminate” to refer towh-words as “nouns that behave like a logical variable.”2

Wh-quantification
We commonly think of question-formation as the primary use ofwh-phrases. But in many languages, wh-phrases are also used forquantification.

(1)

Uses of Japanese dare:(Shimoyama 2006:143)
whda’reinterrogative ‘who’
wh-MO (?) da’re-mo
universal ‘everyone’
wh-DISJ
da’re-ka
existential ‘someone’
wh-EVEN
dare-mo
NPI ‘anyone’
wh-CSP
dare-demo free choice ‘anyone’

Kuroda (1965:43) introduced the term “indeterminate” to refer towh-words as “nouns that behave like a logical variable.”2

Wh-quantification

Many languages combine wh-phrases with other particles to form
quantifiers.
 Two of the most common types of morphemes involved in
wh-quantification are (a) disjunctors and (b) scalar focus
particles (see e.g. Haspelmath 1997:157).
Q: What explains these prevalent combinations? Why theseparticles?

3

Wh-quantification

Many languages combine wh-phrases with other particles to form
quantifiers.
 Two of the most common types of morphemes involved in
wh-quantification are (a) disjunctors and (b) scalar focus
particles (see e.g. Haspelmath 1997:157).
Q: What explains these prevalent combinations? Why theseparticles?

3

Wh-quantification

Many languages combine wh-phrases with other particles to form
quantifiers.
 Two of the most common types of morphemes involved in
wh-quantification are (a) disjunctors and (b) scalar focus
particles (see e.g. Haspelmath 1997:157).
Q: What explains these prevalent combinations? Why theseparticles?

3

TodayI present a framework for the compositional semantics of alternatives
which models various attested forms of wh-quantification, and helps
us the prevalent use of disjunctors and focus particles in
wh-quantification.
Wh-phrases (and disjunctions) introduce alternatives (Hamblin 1973
and many others). I adopt the view that these alternatives areformally the same as (Roothian) alternatives for the computation of
focus (Beck 2006 a.o.).

4

TodayI present a framework for the compositional semantics of alternatives
which models various attested forms of wh-quantification, and helps
us the prevalent use of disjunctors and focus particles in
wh-quantification.
Wh-phrases (and disjunctions) introduce alternatives (Hamblin 1973
and many others). I adopt the view that these alternatives areformally the same as (Roothian) alternatives for the computation of
focus (Beck 2006 a.o.).

4

Today
A: Focus particles (and disjunctions) are unique in quantifying overalternatives. (With some help,) they can quantify overalternatives introduced by wh-phrases, using their regular focus
particle semantics.
• The approach derives common combinations such as
wh-EVEN NPIs and wh-DISJ indefinites, as well as othercombinations such as wh-CLEFT NPIs, wh-ONLY FCIs, andwh-COND-EVEN FCIs.
• Cross-linguistic differences in wh-quantification are due to(a) what (combinations of) operators are spelled out
morphologically and (b) the syntactic distribution of thehelping operators.

5

Today
A: Focus particles (and disjunctions) are unique in quantifying overalternatives. (With some help,) they can quantify overalternatives introduced by wh-phrases, using their regular focus
particle semantics.
• The approach derives common combinations such as
wh-EVEN NPIs and wh-DISJ indefinites, as well as othercombinations such as wh-CLEFT NPIs, wh-ONLY FCIs, andwh-COND-EVEN FCIs.
• Cross-linguistic differences in wh-quantification are due to(a) what (combinations of) operators are spelled out
morphologically and (b) the syntactic distribution of thehelping operators.

5

Today
A: Focus particles (and disjunctions) are unique in quantifying overalternatives. (With some help,) they can quantify overalternatives introduced by wh-phrases, using their regular focus
particle semantics.
• The approach derives common combinations such as
wh-EVEN NPIs and wh-DISJ indefinites, as well as othercombinations such as wh-CLEFT NPIs, wh-ONLY FCIs, andwh-COND-EVEN FCIs.
• Cross-linguistic differences in wh-quantification are due to(a) what (combinations of) operators are spelled out
morphologically and (b) the syntactic distribution of thehelping operators.

5

Roadmap§1 Introduction§2 Alternative Semantics§3 The framework§4 Case studies§5 Variation

6§2 Alternative Semantics

7

Roothian focus semantics(2)

Alternative Semantics (Rooth 1985, 1992):
We keep track of two dimensions of meaning. For any
syntactic object α, we compute:oa. the ordinary semantic value JαK ; andaltb. the alternative set (or focus semantic value) JαK , the setof all ordinary semantic values obtained by substituting
alternatives for any F-marked subparts of α.

8Roothian focus semantics
Consider the contrast below:(3)

Mary only bought a [sandwich]F .

(4)Mary only [bought]F a sandwich.

(3’)

JM bought a [sandwich]F Ko = ∧M bought a sandwich
(prejacent)∧MboughtasandwichT∧JM bought a [sandwich]F Kalt =M bought a pizzaF ∧ M bought a salad
F

Alternative Semantics provides a recursive procedure for computing
these alternative sets, often called “pointwise” or “Hamblin”
composition.
9

Roothian focus semantics
Consider the contrast below:(3)

Mary only bought a [sandwich]F .

(4)Mary only [bought]F a sandwich.

(3’)

JM bought a [sandwich]F Ko = ∧M bought a sandwich
(prejacent)∧MboughtasandwichT∧JM bought a [sandwich]F Kalt =M bought a pizzaF ∧ M bought a salad
F

Alternative Semantics provides a recursive procedure for computing
these alternative sets, often called “pointwise” or “Hamblin”
composition.
9

Roothian focus semantics
Consider the contrast below:(3)

Mary only bought a [sandwich]F .

(4)Mary only [bought]F a sandwich.

(3’)

JM bought a [sandwich]F Ko = ∧M bought a sandwich
(prejacent)∧MboughtasandwichT∧JM bought a [sandwich]F Kalt =M bought a pizzaF ∧ M bought a salad
F

Alternative Semantics provides a recursive procedure for computing
these alternative sets, often called “pointwise” or “Hamblin”
composition.
9

Roothian focus semantics
Consider the contrast below:(3)

Mary only bought a [sandwich]F .

(4)Mary only [bought]F a sandwich.

(3’)

JM bought a [sandwich]F Ko = ∧M bought a sandwich
(prejacent)∧MboughtasandwichT∧JM bought a [sandwich]F Kalt =F
M bought a pizza ∧ M bought a salad
F

Alternative Semantics provides a recursive procedure for computing
these alternative sets, often called “pointwise” or “Hamblin”
composition.
9

Roothian focus semantics
Consider the contrast below:(3)

Mary only bought a [sandwich]F .

(4)Mary only [bought]F a sandwich.

(3’)

JM bought a [sandwich]F Ko = ∧M bought a sandwich
(prejacent)∧MboughtasandwichT∧JM bought a [sandwich]F Kalt =M bought a pizzaF ∧ M bought a salad
F

Alternative Semantics provides a recursive procedure for computing
these alternative sets, often called “pointwise” or “Hamblin”
composition.
9

Roothian focus semantics
Consider the contrast below:(3)

Mary only bought a [sandwich]F .

(4)Mary only [bought]F a sandwich.

(4’)

JM [bought]F a sandwichKo = ∧M bought a sandwich
(prejacent)∧MboughtasandwichT∧JM [bought]F a sandwichKalt =M ate a sandwichF ∧ M sold a sandwich
F

Alternative Semantics provides a recursive procedure for computing
these alternative sets, often called “pointwise” or “Hamblin”
composition.
9

Roothian focus semantics
Consider the contrast below:(3)

Mary only bought a [sandwich]F .

(4)Mary only [bought]F a sandwich.

(4’)

JM [bought]F a sandwichKo = ∧M bought a sandwich
(prejacent)∧MboughtasandwichT∧JM [bought]F a sandwichKalt =M ate a sandwichF ∧ M sold a sandwich
F

Alternative Semantics provides a recursive procedure for computing
these alternative sets, often called “pointwise” or “Hamblin”
composition.
9

Roothian focus semantics

(5)

r

only

α

zo

= λw . ∀q ∈ JαK

altoq 6= JαK → q(w) = 0

“All non-prejacent alternatives are false”o; presupposition: JαK (w) = 1
(6)

s

even

α

{o

= JαK

o


alt 
o
o
; presup.: ∀q ∈ JαK q 6= JαK → JαK <likely q“The prejacent is the least likely alternative.”10

Roothian focus semantics

(5)

r

only

α

zo

= λw . ∀q ∈ JαK

altoq 6= JαK → q(w) = 0

“All non-prejacent alternatives are false”o; presupposition: JαK (w) = 1
(6)

s

even

α

{o

= JαK

o


alt 
o
o
; presup.: ∀q ∈ JαK q 6= JαK → JαK <likely q“The prejacent is the least likely alternative.”10Three details of noteoalt

1. Under this Roothian framework, any α satisfies JαK ∈ JαK . I
codify this as a requirement that every clause satisfy (7):(7)

Interpretability:(based on Rooth 1992; Beck 2006)oalt
To interpret α, JαK must be defined and ∈ JαK .

2. Focus particles are unique in being able to look at alternativealt
sets (J...K ). Other lexical items simply compose pointwise.
3. Once alternatives from a particular focus are “used” by a focus
particle, those alternatives cannot be interpreted again by ahigher operator. All focus particles are “resetting”:(8)

Reset:
alto
Op is “resetting” if it specifies JOp αK := JOp αK .

11Three details of noteoalt

1. Under this Roothian framework, any α satisfies JαK ∈ JαK . I
codify this as a requirement that every clause satisfy (7):(7)

Interpretability:(based on Rooth 1992; Beck 2006)oalt
To interpret α, JαK must be defined and ∈ JαK .

2. Focus particles are unique in being able to look at alternativealt
sets (J...K ). Other lexical items simply compose pointwise.
3. Once alternatives from a particular focus are “used” by a focus
particle, those alternatives cannot be interpreted again by ahigher operator. All focus particles are “resetting”:(8)

Reset:
alto
Op is “resetting” if it specifies JOp αK := JOp αK .

11Three details of noteoalt

1. Under this Roothian framework, any α satisfies JαK ∈ JαK . I
codify this as a requirement that every clause satisfy (7):(7)

Interpretability:(based on Rooth 1992; Beck 2006)oalt
To interpret α, JαK must be defined and ∈ JαK .

2. Focus particles are unique in being able to look at alternativealt
sets (J...K ). Other lexical items simply compose pointwise.
3. Once alternatives from a particular focus are “used” by a focus
particle, those alternatives cannot be interpreted again by ahigher operator. All focus particles are “resetting”:(8)

Reset:
alto
Op is “resetting” if it specifies JOp αK := JOp αK .

11

Neo-Hamblin question semantics

Hamblin 1973 proposed that the meaning of a question is the set of
possible answer propositions.

(9)



∧

 Alex likes Bobby, ∧JWho does Alex like?K =Alex likes Chris, ∧ Alex likes Dana,... Here I present a modern implementation of this idea in the Roothian
two-dimensional semantics.

12

Neo-Hamblin question semantics

A wh-phrase has a set of possible values (≈ short answers) as its
alternative set, with no defined ordinary semantic value (Ramchand
1997; Beck 2006):o(10) JwhoK is undefinedalt
JwhoK = {xe : x is human}13

Neo-Hamblin question semantics

(11)

o

a. JAlex likes whoK is undefined∧ Alex likes Bobby, 
alt∧b. JAlex likes whoK =Alex likes Chris, ∧ Alex likes Dana 

But (11) has no ordinary semantic value and violates Interpretability!

14

Neo-Hamblin question semantics

(11)

o

a. JAlex likes whoK is undefined∧ Alex likes Bobby, 
alt∧b. JAlex likes whoK =Alex likes Chris, ∧ Alex likes Dana 

But (11) has no ordinary semantic value and violates Interpretability!

14

Neo-Hamblin question semantics

(11)

o

a. JAlex likes whoK is undefined∧ Alex likes Bobby, 
alt∧b. JAlex likes whoK =Alex likes Chris, ∧ Alex likes Dana 

But (11) has no ordinary semantic value and violates Interpretability!

14

Neo-Hamblin question semantics

An operator “lifts” the meaning in (11) into an Interpretable question
meaning:(12)

A LT S HIFT (Kotek 2016, 2019):oalt

a. J[A LT S HIFT α]K = JαK
n
o
alt
alt
b. J[A LT S HIFT α]K = JαK← reset15

Neo-Hamblin question semantics

An operator “lifts” the meaning in (11) into an Interpretable question
meaning:(12)

A LT S HIFT (Kotek 2016, 2019):oalt

a. J[A LT S HIFT α]K = JαK
n
o
alt
alt
b. J[A LT S HIFT α]K = JαK← reset15

Neo-Hamblin question semantics

(13)



∧

 Alex likes Bobby, o∧a. JA LT S HIFT [Alex likes who]K =Alex likes Chris, ∧ Alex likes Dana 



∧




 Alex likes Bobby, 
alt∧b. JA LT S HIFT [Alex likes who]K =Alex likes Chris,




 ∧ Alex likes Dana 

16Disjunction in Alternative Semantics

Alonso-Ovalle (2004) and Aloni (2007) propose that alternative setsare used for the interpretation of disjunction and its scope-taking,using a one-dimensional Hamblin semantics. They split disjunction
into two steps:
1. A junctor head J (Den Dikken 2006 a.o.) creates an alternative
set over its disjuncts;
2. an ∃ operator combines these alternatives by disjunction.

17

Disjunction in Alternative Semantics

Alonso-Ovalle (2004) and Aloni (2007) propose that alternative setsare used for the interpretation of disjunction and its scope-taking,using a one-dimensional Hamblin semantics. They split disjunction
into two steps:
1. A junctor head J (Den Dikken 2006 a.o.) creates an alternative
set over its disjuncts;
2. an ∃ operator combines these alternatives by disjunction.

17

Disjunction in Alternative Semantics

Alonso-Ovalle (2004) and Aloni (2007) propose that alternative setsare used for the interpretation of disjunction and its scope-taking,using a one-dimensional Hamblin semantics. They split disjunction
into two steps:
1. A junctor head J (Den Dikken 2006 a.o.) creates an alternative
set over its disjuncts;
2. an ∃ operator combines these alternatives by disjunction.

17

Disjunction in Alternative Semantics
Let’s translate this intuition into the two-dimensional Alternative
Semantics framework. J forms an expression with no ordinary value,
like wh-phrases:

(15)

o

a. JJ {Bobby, Chris}K undefinedb. JJ {Bobby, Chris}K

(16)

alt

= {Bobby, Chris}oa. JAlex likes [Bobby orJ Chris]K undefined()∧
Alex likes Bobby,
altb. JAlex likes [Bobby orJ Chris]K = ∧Alex likes Chris

Now what will ∃ look like in our two-dimensional framework?
18

Disjunction in Alternative Semantics
Let’s translate this intuition into the two-dimensional Alternative
Semantics framework. J forms an expression with no ordinary value,
like wh-phrases:

(15)

o

a. JJ {Bobby, Chris}K undefinedb. JJ {Bobby, Chris}K

(16)

alt

= {Bobby, Chris}oa. JAlex likes [Bobby orJ Chris]K undefined()∧
Alex likes Bobby,
altb. JAlex likes [Bobby orJ Chris]K = ∧Alex likes Chris

Now what will ∃ look like in our two-dimensional framework?
18∃ option 1(17) ∃ with argument α :Woalta. J∃ αK = JαK
alt

b. J∃ αK

(18)

alt

= JαK

o

a. J∃ [A likes [B orJ C]]K = ∧ A likes B ∨ A likes C)(∧
Alex likes Bobby,
altb. J∃ [A likes [B orJ C]]K = ∧Alex likes Chris

But (18) violates Interpretability (7)!

19∃ option 1(17) ∃ with argument α :Woalta. J∃ αK = JαK
alt

b. J∃ αK

(18)

alt

= JαK

o

a. J∃ [A likes [B orJ C]]K = ∧ A likes B ∨ A likes C)(∧
Alex likes Bobby,
altb. J∃ [A likes [B orJ C]]K = ∧Alex likes Chris

But (18) violates Interpretability (7)!

19∃ option 1(17) ∃ with argument α :Woalta. J∃ αK = JαK
alt

b. J∃ αK

(18)

alt

= JαK

o

a. J∃ [A likes [B orJ C]]K = ∧ A likes B ∨ A likes C)(∧
Alex likes Bobby,
altb. J∃ [A likes [B orJ C]]K = ∧Alex likes Chris

But (18) violates Interpretability (7)!

19∃ option 1(17) ∃ with argument α :Woalta. J∃ αK = JαK
alt

b. J∃ αK

(18)

alt

= JαK

o

a. J∃ [A likes [B orJ C]]K = ∧ A likes B ∨ A likes C)(∧
Alex likes Bobby,
altb. J∃ [A likes [B orJ C]]K = ∧Alex likes Chris

But (18) violates Interpretability (7)!

19∃ option 2

A version of ∃ which is “resetting” would fix this problem:(19) ∃ reset with argument α :Woalta. J∃reset αK = JαK
o
nW
alt
alt
JαK
b. J∃reset αK =(20)

← resetoa. J∃reset [A likes [B orJ C]]K = ∧ A likes B ∨ A likes C
b. J∃reset [A likes [B orJ C]]Kalt

= {∧ A likes B ∨ A likes C}20

∃ option 2

A version of ∃ which is “resetting” would fix this problem:(19) ∃ reset with argument α :Woalta. J∃reset αK = JαK
o
nW
alt
alt
JαK
b. J∃reset αK =(20)

← resetoa. J∃reset [A likes [B orJ C]]K = ∧ A likes B ∨ A likes C
b. J∃reset [A likes [B orJ C]]Kalt

= {∧ A likes B ∨ A likes C}20

§3 The framework

21

The framework

A wh/J-containing clause has a non-singleton alternative set and no
defined ordinary semantic value:

(21)

o

a. J[TP ... wh/J ... ]K undefinedb. J[TP ... wh/J ... ]Kalt= {p, q, ...}(a set of propositions)This violates Interpretability (7)! In particular, we need to compute an
ordinary semantic value based on (21).

22The framework

A wh/J-containing clause has a non-singleton alternative set and no
defined ordinary semantic value:

(21)

o

a. J[TP ... wh/J ... ]K undefinedb. J[TP ... wh/J ... ]Kalt= {p, q, ...}(a set of propositions)This violates Interpretability (7)! In particular, we need to compute an
ordinary semantic value based on (21).

22The framework

 I propose that A LT S HIFT, ∃, and ∃reset are the only operatorsthat can define an ordinary semantic value where there isnone.
• We can apply A LT S HIFT to (21) get an Interpretable question or
apply ∃reset to get an Interpretable existential/disjunctive
proposition.

23

The framework

 I propose that A LT S HIFT, ∃, and ∃reset are the only operatorsthat can define an ordinary semantic value where there isnone.
• We can apply A LT S HIFT to (21) get an Interpretable question or
apply ∃reset to get an Interpretable existential/disjunctive
proposition.

23

The framework• We could apply ∃ to (21) to define an ordinary semantic value,
but this result (22) will still violate Interpretability!
(22)oa. J∃ [TP ... wh/J ... ]K = p ∨ q ∨ ...
b. J∃ [TP ... wh/J ... ]Kalt= {p, q, ...}• We can then apply a focus particle, which will fix theInterpretability problem, because it “resets” (8) thealternative set.
• Focus particles can’t apply directly to (21) because there isno defined ordinary value (prejacent).

24

The framework• We could apply ∃ to (21) to define an ordinary semantic value,
but this result (22) will still violate Interpretability!
(22)oa. J∃ [TP ... wh/J ... ]K = p ∨ q ∨ ...
b. J∃ [TP ... wh/J ... ]Kalt= {p, q, ...}• We can then apply a focus particle, which will fix theInterpretability problem, because it “resets” (8) thealternative set.
• Focus particles can’t apply directly to (21) because there isno defined ordinary value (prejacent).

24

The framework• We could apply ∃ to (21) to define an ordinary semantic value,
but this result (22) will still violate Interpretability!
(22)oa. J∃ [TP ... wh/J ... ]K = p ∨ q ∨ ...
b. J∃ [TP ... wh/J ... ]Kalt= {p, q, ...}• We can then apply a focus particle, which will fix theInterpretability problem, because it “resets” (8) thealternative set.
• Focus particles can’t apply directly to (21) because there isno defined ordinary value (prejacent).

24

§4 Case studies

25

Case studies§4.1 Wh-indefinites:
bare wh and wh-DISJ§4.2 Wh-NPIs:
wh-EVEN and wh-CLEFT§4.3 Wh-FCIs:
wh-ONLY and wh-COND-EVEN, etc.
Highlighting data from three Tibeto-Burman languages.

26

Wh-indefinites

Since J-disjunctions and wh-phrases create similar meanings, alanguage could apply ∃reset to a wh-containing clause.

(23)

o

a. J∃reset [Alex likes who]K= ∧ Alex likes Bobby ∨ Alex likes Chris ∨ Alex likes Dana
= ∧ Alex likes someoneb. J∃reset [Alex likes who]Kalt= {∧ Alex likes someone} ← reset27

Wh-indefinites

Since J-disjunctions and wh-phrases create similar meanings, alanguage could apply ∃reset to a wh-containing clause.

(23)

o

a. J∃reset [Alex likes who]K= ∧ Alex likes Bobby ∨ Alex likes Chris ∨ Alex likes Dana
= ∧ Alex likes someoneb. J∃reset [Alex likes who]Kalt= {∧ Alex likes someone} ← reset

27

Bare wh indefinites

 We yield bare wh indefinites if:• J↔ disjunctive particle, e.g. “or”
• ∃reset ↔ ∅28

Wh-disjunctor indefinites
As Haspelmath (1997), Bhat (2000), and others note, many
languages use wh-phrases together with disjunctive particles as
indefinites:(24) Some wh-disjunctor indefinites:‘who’ ‘someone’
Hungarian ki
vala-ki(Szabolcsi 2015)
Japanesedare
da’re-ka(Shimoyama 2006)
Kannadayaaru yaar-oo(Amritavalli 2003)
Tiwa
shar
shar-khi(Dawson to appear) In these languages, the pronunciation of disjunction reflects theuse of ∃reset , even in the absence of J:• J↔∅• ∃reset ↔ disjunctive particle29

Wh-disjunctor indefinites
As Haspelmath (1997), Bhat (2000), and others note, many
languages use wh-phrases together with disjunctive particles as
indefinites:(24) Some wh-disjunctor indefinites:‘who’ ‘someone’
Hungarian ki
vala-ki(Szabolcsi 2015)
Japanesedare
da’re-ka(Shimoyama 2006)
Kannadayaaru yaar-oo(Amritavalli 2003)
Tiwa
shar
shar-khi(Dawson to appear) In these languages, the pronunciation of disjunction reflects theuse of ∃reset , even in the absence of J:• J↔∅• ∃reset ↔ disjunctive particle29

Wh-indefinites in Tiwa

Tiwa (Tibeto-Burman; Dawson 2019, to appear) offers a niceexample of the disjunctor as the realization of (versions of) ∃reset :(25) Two types of wh-indefinites (Dawson to appear):Maria shar -pha/khı́-go lak mán-ga.
Maria who-KHI / PHA-ACC meet-PFV‘Maria met someone.’30

Wh-indefinites in Tiwa

(26) Wh-pha takes narrow scope; wh-khı́ takes wide scope:
Chidı̂ [shar -pha/khı́ sister]-go lak mán-a phi-gaido, Saldi khúpif
who-PHA / KHI sister-ACC meet-INF come-COND Saldi verykhâdu-gam.
happy-CF‘If Saldi meets some nun, she would be very happy.’
a. -pha ⇔ if > ∃: Meeting any nun will make Saldi happy.
b. -khı́ ⇔ ∃ > if: There is a nun that Saldi wants to meet.

31

Wh-indefinites in Tiwa

(26) Wh-pha takes narrow scope; wh-khı́ takes wide scope:
Chidı̂ [shar -pha/khı́ sister]-go lak mán-a phi-gaido, Saldi khúpif
who-PHA / KHI sister-ACC meet-INF come-COND Saldi verykhâdu-gam.
happy-CF‘If Saldi meets some nun, she would be very happy.’
a. -pha ⇔ if > ∃: Meeting any nun will make Saldi happy.
b. -khı́ ⇔ ∃ > if: There is a nun that Saldi wants to meet.

31

Wh-indefinites in Tiwa

(26) Wh-pha takes narrow scope; wh-khı́ takes wide scope:
Chidı̂ [shar -pha/khı́ sister]-go lak mán-a phi-gaido, Saldi khúpif
who-PHA / KHI sister-ACC meet-INF come-COND Saldi verykhâdu-gam.
happy-CF‘If Saldi meets some nun, she would be very happy.’
a. -pha ⇔ if > ∃: Meeting any nun will make Saldi happy.
b. -khı́ ⇔ ∃ > if: There is a nun that Saldi wants to meet.

31

Wh-indefinites in Tiwa
 This correlates with the scope-taking behavior of two different
disjunctions: ba and khi, related to wh-pha and wh-khı́!

(27) Ba disjunction takes narrow scope; khi takes wide scope:
Mukton ba/khi Monbor phi-gaido, Saldi khâdu-gam.
Mukton BA / KHI Monbor come-COND Saldi happy-CF‘If Mukton or Monbor comes, Saldi would be happy.’
a. ba ⇔ if > ∨: Saldi is in love with both Mukton and Monbor.
She will be happy if either of them comes.
b. khi ⇔ ∨ > if: Saldi is in love with either Mukton or
Monbor, but we don’t know who. Whoever it is, if hecomes to visit, Saldi will be very happy.
32

Wh-indefinites in Tiwa

See Dawson 2018, to appear for additional scope facts.
 The uniform wide scope of khi/wh-khi and narrow scope ofba/wh-pha can be explained if khi and ba/pha realize different
forms of ∃reset :• ∃reset with widest scope ↔ khi• ∃reset with narrow scope ↔ ba/pha

33

Wh-EVEN NPIs

NPIs have often been analyzed as involving an overt or covert even.
 An NPI is an even associating with an indefinite.
See e.g. Heim 1984; Krifka 1994; Lee and Horn 1995; Lahiri
1998; Chierchia 2013.

34

EVEN in NPIs

Here’s our basic semantics for even, repeated from above:

(6)

s

even

α

{o

= JαK

o


alt 
o
o
; presup.: ∀q ∈ JαK q 6= JαK → JαK <likely q“The prejacent is the least likely alternative.”
The scalar meaning of even associated with an indefinite will beunsatisfiable, unless it’s in a downward-entailing environment (Lahiri
1998), explaining NPI behavior (Ladusaw 1979).

35

EVEN in NPIs

(28)

* [EVEN [I saw SOMEONE]] ∧ I saw someone, 


alt
∧
JI saw SOMEONEK =I saw many, ∧ I saw everyone ∧∧EVEN ; ( I saw someone) <likely ( I saw many) and(∧ I saw someone) <likely (∧ I saw everyone)

×This presupposition is unsatisfiable, in any context!

36

EVEN in NPIs

(28)

* [EVEN [I saw SOMEONE]] ∧ I saw someone, 


alt
∧
JI saw SOMEONEK =I saw many, ∧ I saw everyone ∧∧EVEN ; ( I saw someone) <likely ( I saw many) and(∧ I saw someone) <likely (∧ I saw everyone)

×This presupposition is unsatisfiable, in any context!

36

EVEN in NPIs

(28)

* [EVEN [I saw SOMEONE]] ∧ I saw someone, 


alt
∧
JI saw SOMEONEK =I saw many, ∧ I saw everyone ∧∧EVEN ; ( I saw someone) <likely ( I saw many) and(∧ I saw someone) <likely (∧ I saw everyone)

×This presupposition is unsatisfiable, in any context!

36

EVEN in NPIs

(28)

* [EVEN [I saw SOMEONE]] ∧ I saw someone, 


alt
∧
JI saw SOMEONEK =I saw many, ∧ I saw everyone ∧∧EVEN ; ( I saw someone) <likely ( I saw many) and(∧ I saw someone) <likely (∧ I saw everyone)

×This presupposition is unsatisfiable, in any context!

36

EVEN in NPIs

(29)

X

[EVEN [NEG [I see SOMEONE]]
= “I didn’t see anyone.” ∧ NEG( I saw someone), alt
JNEG [I saw SOMEONE]K =NEG (∧ I saw many), NEG(∧ I saw everyone) 
EVEN ; ¬(∧ I saw someone) <likely ¬(∧ I saw many) and¬(∧ I saw someone) <likely ¬(∧ I saw everyone)⇐⇒ (∧ I saw someone) >likely (∧ I saw many) and(∧ I saw someone) >likely (∧ I saw everyone)37

EVEN in NPIs

(29)

X

[EVEN [NEG [I see SOMEONE]]
= “I didn’t see anyone.” ∧ NEG( I saw someone), alt
JNEG [I saw SOMEONE]K =NEG (∧ I saw many), NEG(∧ I saw everyone) 
EVEN ; ¬(∧ I saw someone) <likely ¬(∧ I saw many) and¬(∧ I saw someone) <likely ¬(∧ I saw everyone)⇐⇒ (∧ I saw someone) >likely (∧ I saw many) and(∧ I saw someone) >likely (∧ I saw everyone)37

EVEN in NPIs

(29)

X

[EVEN [NEG [I see SOMEONE]]
= “I didn’t see anyone.” ∧ NEG( I saw someone), alt
JNEG [I saw SOMEONE]K =NEG (∧ I saw many), NEG(∧ I saw everyone) 
EVEN ; ¬(∧ I saw someone) <likely ¬(∧ I saw many) and¬(∧ I saw someone) <likely ¬(∧ I saw everyone)⇐⇒ (∧ I saw someone) >likely (∧ I saw many) and(∧ I saw someone) >likely (∧ I saw everyone)37

EVEN in NPIs

(29)

X

[EVEN [NEG [I see SOMEONE]]
= “I didn’t see anyone.” ∧ NEG( I saw someone), alt
JNEG [I saw SOMEONE]K =NEG (∧ I saw many), NEG(∧ I saw everyone) 
EVEN ; ¬(∧ I saw someone) <likely ¬(∧ I saw many) and¬(∧ I saw someone) <likely ¬(∧ I saw everyone)⇐⇒ (∧ I saw someone) >likely (∧ I saw many) and(∧ I saw someone) >likely (∧ I saw everyone)37

EVEN in NPIs

(29)

X

[EVEN [NEG [I see SOMEONE]]
= “I didn’t see anyone.” ∧ NEG( I saw someone), alt
JNEG [I saw SOMEONE]K =NEG (∧ I saw many), NEG(∧ I saw everyone) 
EVEN ; ¬(∧ I saw someone) <likely ¬(∧ I saw many) and¬(∧ I saw someone) <likely ¬(∧ I saw everyone)⇐⇒ (∧ I saw someone) >likely (∧ I saw many) and(∧ I saw someone) >likely (∧ I saw everyone)37

Wh-EVEN NPIs

Tibetan (Erlewine and Kotek 2016) has wh-(one)-EVEN NPIs but barewh-(one) are not indefinites.

(30) Tibetan wh, indefinites, and NPIs:
su ‘who’mi-gcig “person-one” ‘someone’su-yang ‘anyone’gare ‘what’ (calag)-gcig “(thing)-one” ‘something’ gare-yang ‘anything’(31) Su-yang slebs-ma-song / *slebs-song.
who-EVEN arrive-NEG-PRFV / *arrive-PRFV‘No one arrived.’38

Wh-EVEN NPIs

 Tibetan a free covert ∃ but not ∃ reset .
(32)

oa. J∃ [who arrived]K = ∧ someone arrived


∧


 A arrived,alt∧b. J∃ [who arrived]K =B arrived, ∧ C arrived, ... × Violates Interpretability (7)!

39

Wh-EVEN NPIs

 Tibetan a free covert ∃ but not ∃ reset .
(32)

oa. J∃ [who arrived]K = ∧ someone arrived


∧


 A arrived,alt∧b. J∃ [who arrived]K =B arrived, ∧ C arrived, ... × Violates Interpretability (7)!

39

Wh-EVEN NPIs

 Tibetan a free covert ∃ but not ∃ reset .
(32)

oa. J∃ [who arrived]K = ∧ someone arrived


∧


 A arrived,alt∧b. J∃ [who arrived]K =B arrived, ∧ C arrived, ... × Violates Interpretability (7)!

39

Wh-EVEN NPIs

We can fix this Interpretability problem with EVEN, because it’sresetting:

(33)

o

a. JEVEN [∃ [who arrived]]K = ∧ someone arrived
EVEN ; ∀x [(∧ someone arrived) <likely (∧ x arrived)]alt

b. JEVEN [∃ [who arrived]]K = {∧ someone arrived}
Interpretable; × Unsatisfiable presupposition!

40

Wh-EVEN NPIs

We can fix this Interpretability problem with EVEN, because it’sresetting:

(33)

o

a. JEVEN [∃ [who arrived]]K = ∧ someone arrived
EVEN ; ∀x [(∧ someone arrived) <likely (∧ x arrived)]alt

b. JEVEN [∃ [who arrived]]K = {∧ someone arrived}
Interpretable; × Unsatisfiable presupposition!

40

Wh-EVEN NPIs

We can fix this Interpretability problem with EVEN, because it’sresetting:

(33)

o

a. JEVEN [∃ [who arrived]]K = ∧ someone arrived
EVEN ; ∀x [(∧ someone arrived) <likely (∧ x arrived)]alt

b. JEVEN [∃ [who arrived]]K = {∧ someone arrived}
Interpretable; × Unsatisfiable presupposition!

40

Wh-EVEN NPIs

We additionally need a downward-entailing operator to get asatisfiable presupposition:

(34)

o

a. JEVEN [NEG[∃ [who arrived]]]K = ∧ no one arrived
EVEN ; ∀x [¬(∧ someone arrived) <likely ¬(∧ x arrived)]alt

b. JEVEN [NEG[∃ [who arrived]]]K = {∧ no one arrived}
Interpretable;
Satisfiable (tautological) presupposition

41

Wh-EVEN NPIs

We additionally need a downward-entailing operator to get asatisfiable presupposition:

(34)

o

a. JEVEN [NEG[∃ [who arrived]]]K = ∧ no one arrived
EVEN ; ∀x [¬(∧ someone arrived) <likely ¬(∧ x arrived)]alt

b. JEVEN [NEG[∃ [who arrived]]]K = {∧ no one arrived}
Satisfiable (tautological) presupposition
Interpretable;

41

Wh-EVEN NPIs

 This explains why the use of EVEN is obligatory in wh-EVEN NPIs,
even though the addition of EVEN does not make a contribution
to the overall meaning expressed. E VEN repairs the violation ofInterpretability.

42

Wh-CLEFT NPIs

Burmese forms wh-NPIs with a cleft semantics particle, hma:(35) Burmesehmas{o (New and Erlewine 2018):ohma α = λw . JαK (w); presup.: ∀q ∈ JαKaltq <likely JαKo → q(w) = 0“All less likely alternatives are false.”

This is similar to the semantics for it-clefts in Velleman et al. 2012.

43

Wh-CLEFT NPIs

(36)

Nga-ga [bal panthi]-ko-hma ma-yu-keh-bu/
1-NOM which apple-ACC-HMA NEG-take-PAST-NEG /*yu-keh-deh.
*take-PAST-REAL‘I didn’t take any apple(s).’44Wh-CLEFT NPIs
Wh-CLEFT NPIs can also be derived within our framework.
 Burmese has free covert ∃ but not ∃ reset .
Let 1, 2, and 3 be apples in the context.

(37)

o

a. J∃ [I took which apple]K = ∧ I took 1 ∨ I took 2 ∨ I took 3∧ I took 1, alt∧b. J∃ [I took which apple]K =I took 2, ∧ I took 3 × Violates Interpretability (7)45Wh-CLEFT NPIs
Wh-CLEFT NPIs can also be derived within our framework.
 Burmese has free covert ∃ but not ∃ reset .
Let 1, 2, and 3 be apples in the context.

(37)

o

a. J∃ [I took which apple]K = ∧ I took 1 ∨ I took 2 ∨ I took 3∧ I took 1, alt∧b. J∃ [I took which apple]K =I took 2, ∧ I took 3 × Violates Interpretability (7)45Wh-CLEFT NPIs
Now apply hma applying to (37), with and without higher negation:o(38)* JHMA [∃ [I took which apple]]K = ∧ I took some apple
HMA ; ¬1 ∧ ¬2 ∧ ¬3
Interpretable;
× Assertion incompatible with presupposition(39)

JNEG [HMA [∃ [I took which apple]]]K= ¬ [I took some apple] = ∧ I didn’t take any apple
HMA ; ¬1 ∧ ¬2 ∧ ¬3
Interpretable;
Assertion compatible with presuppositiono46

Wh-CLEFT NPIs
Now apply hma applying to (37), with and without higher negation:o(38)* JHMA [∃ [I took which apple]]K = ∧ I took some apple
HMA ; ¬1 ∧ ¬2 ∧ ¬3
Interpretable;
× Assertion incompatible with presupposition(39)

JNEG [HMA [∃ [I took which apple]]]K= ¬ [I took some apple] = ∧ I didn’t take any apple
HMA ; ¬1 ∧ ¬2 ∧ ¬3
Interpretable;
Assertion compatible with presuppositiono46

Wh-CLEFT NPIs
Now apply hma applying to (37), with and without higher negation:o(38)* JHMA [∃ [I took which apple]]K = ∧ I took some apple
HMA ; ¬1 ∧ ¬2 ∧ ¬3
Interpretable;
× Assertion incompatible with presupposition(39)

JNEG [HMA [∃ [I took which apple]]]K= ¬ [I took some apple] = ∧ I didn’t take any apple
HMA ; ¬1 ∧ ¬2 ∧ ¬3
Interpretable;
Assertion compatible with presuppositiono46

Wh-FCIs

There are many different FCIs formed from wh-phrases with someparticle (Giannakidou and Cheng 2006):
1. Wh-“modal particle”: e.g. English who-ever, Greek
opjos-dhipote,...
2. Wh-DISJ: e.g. Korean nwukwu-na (Gill et al. 2006; Kim andKaufmann 2006; Choi 2007; Choi and Romero 2008; a.o.)
3. Wh-THEN-ALSO: e.g. Dutch wie den ook (Rullmann 1996)
Here, I mention two patterns not mentioned in Giannakidou andCheng 2006:

47

Wh-FCIs

There are many different FCIs formed from wh-phrases with someparticle (Giannakidou and Cheng 2006):
1. Wh-“modal particle”: e.g. English who-ever, Greek
opjos-dhipote,...
2. Wh-DISJ: e.g. Korean nwukwu-na (Gill et al. 2006; Kim andKaufmann 2006; Choi 2007; Choi and Romero 2008; a.o.)
3. Wh-THEN-ALSO: e.g. Dutch wie den ook (Rullmann 1996)
Here, I mention two patterns not mentioned in Giannakidou andCheng 2006:

47

Wh-FCIs(40) Burmese wh-ONLY FCI:

(Keely New, p.c.)

Nga [bal hin]-beh sar-lo ya-dal.
1
which dish-ONLY eat-C get-REAL‘I can eat any dish.’ The use of an exhaustive particle (ONLY) in the expression of freechoice can be understood under the exhaustification approach to
free choice (Fox 2007), and can be modeled under this proposal.
See Appendix A.
Chuj (Mayan; Kotek and Erlewine 2019) also forms FCIs with wh +ONLY .
48

Wh-FCIs(40) Burmese wh-ONLY FCI:

(Keely New, p.c.)

Nga [bal hin]-beh sar-lo ya-dal.
1
which dish-ONLY eat-C get-REAL‘I can eat any dish.’ The use of an exhaustive particle (ONLY) in the expression of freechoice can be understood under the exhaustification approach to
free choice (Fox 2007), and can be modeled under this proposal.
See Appendix A.
Chuj (Mayan; Kotek and Erlewine 2019) also forms FCIs with wh +ONLY .
48

Wh-FCIs(40) Burmese wh-ONLY FCI:

(Keely New, p.c.)

Nga [bal hin]-beh sar-lo ya-dal.
1
which dish-ONLY eat-C get-REAL‘I can eat any dish.’ The use of an exhaustive particle (ONLY) in the expression of freechoice can be understood under the exhaustification approach to
free choice (Fox 2007), and can be modeled under this proposal.
See Appendix A.
Chuj (Mayan; Kotek and Erlewine 2019) also forms FCIs with wh +ONLY .
48

Wh-FCIs(41) Tibetan wh-COP-COND-EVEN FCI:

(Erlewine 2019)

Mo.rang [su yin-na]-yang-laskad.cha bshad-gi-red.
she
who COP-COND-EVEN-DAT speech talk-IMPF-AUX[Pema is very friendly.] ‘She talks to anyone.’ Even if combinations are concessive conditionals, which canalso form unconditionals. Yin-na-yang also functions as aconcessive scalar particle. See Appendix B for my analysis.
And similarly in Dravidian (Rahul Balusu, yesterday)!

49

Wh-FCIs(41) Tibetan wh-COP-COND-EVEN FCI:

(Erlewine 2019)

Mo.rang [su yin-na]-yang-laskad.cha bshad-gi-red.
she
who COP-COND-EVEN-DAT speech talk-IMPF-AUX[Pema is very friendly.] ‘She talks to anyone.’ Even if combinations are concessive conditionals, which canalso form unconditionals. Yin-na-yang also functions as aconcessive scalar particle. See Appendix B for my analysis.
And similarly in Dravidian (Rahul Balusu, yesterday)!

49

Wh-FCIs(41) Tibetan wh-COP-COND-EVEN FCI:

(Erlewine 2019)

Mo.rang [su yin-na]-yang-laskad.cha bshad-gi-red.
she
who COP-COND-EVEN-DAT speech talk-IMPF-AUX[Pema is very friendly.] ‘She talks to anyone.’ Even if combinations are concessive conditionals, which canalso form unconditionals. Yin-na-yang also functions as aconcessive scalar particle. See Appendix B for my analysis.
And similarly in Dravidian (Rahul Balusu, yesterday)!

49

§5 Accounting for variation50

Accounting for variation

Not all languages have the same range of wh-particle quantifier
combinations. How do languages vary?
1

Differences in what (combinations of) operators are spelled out
morphologically; and2syntactic restrictions on the placement of A LT S HIFT, ∃, ∃reset .

51

Accounting for variation

Not all languages have the same range of wh-particle quantifier
combinations. How do languages vary?
1

Differences in what (combinations of) operators are spelled out
morphologically; and2syntactic restrictions on the placement of A LT S HIFT, ∃, ∃reset .

51

Different lexicalizations

We already saw this in §1: A disjunctive particle could morphologicallyrealize J or ∃reset , the two ingredients in boolean disjunction.
The framework can also model more complex inventories...

52Different lexicalizations

We already saw this in §1: A disjunctive particle could morphologicallyrealize J or ∃reset , the two ingredients in boolean disjunction.
The framework can also model more complex inventories...

52

Toba Batak manang (Erlewine 2017a)
Toba Batak (Austronesian; Indonesia) has a particle manang whichforms disjunctions but also forms wh-NPI/FCIs.

(42)

Man-uhor buku i[ho manang ahu].
ACT -buy book that 2sg MANANG 1sg‘Either you or I bought the book.’(43)

Si Poltak (dang) mang-allang [manang aha].
PN Poltak NEG ACT-eat
MANANG what
‘Poltak {doesn’t eat / eats} anything.’

 manang ↔ J or ∃. See Erlewine 2017a.
53

Toba Batak manang (Erlewine 2017a)
Toba Batak (Austronesian; Indonesia) has a particle manang whichforms disjunctions but also forms wh-NPI/FCIs.

(42)

Man-uhor buku i[ho manang ahu].
ACT -buy book that 2sg MANANG 1sg‘Either you or I bought the book.’(43)

Si Poltak (dang) mang-allang [manang aha].
PN Poltak NEG ACT-eat
MANANG what
‘Poltak {doesn’t eat / eats} anything.’

 manang ↔ J or ∃. See Erlewine 2017a.
53

Two disjunctors in Mandarin (Erlewine 2017b)

Mandarin has two disjunctors: háishi generally forms alternative
questions, whereas huòzhe expresses logical disjunction, leading toproposals that háishi but not huòzhe has a [+wh] feature (Huang
1982, a.o.).
But the difference is neutralized in certain environments! These are,for many speakers, the same environments where wh-phrases also
have non interrogative uses.
 Háishi and huòzhe are both J, but huòzhe has a [u∃] feature
which requires a local ∃ or ∃reset . See Erlewine 2017b.

54

Two disjunctors in Mandarin (Erlewine 2017b)

Mandarin has two disjunctors: háishi generally forms alternative
questions, whereas huòzhe expresses logical disjunction, leading toproposals that háishi but not huòzhe has a [+wh] feature (Huang
1982, a.o.).
But the difference is neutralized in certain environments! These are,for many speakers, the same environments where wh-phrases also
have non interrogative uses.
 Háishi and huòzhe are both J, but huòzhe has a [u∃] feature
which requires a local ∃ or ∃reset . See Erlewine 2017b.

54

Two disjunctors in Mandarin (Erlewine 2017b)

Mandarin has two disjunctors: háishi generally forms alternative
questions, whereas huòzhe expresses logical disjunction, leading toproposals that háishi but not huòzhe has a [+wh] feature (Huang
1982, a.o.).
But the difference is neutralized in certain environments! These are,for many speakers, the same environments where wh-phrases also
have non interrogative uses.
 Háishi and huòzhe are both J, but huòzhe has a [u∃] feature
which requires a local ∃ or ∃reset . See Erlewine 2017b.

54

Different syntactic restrictions

One example: In many languages with bare wh indefinites, they are
limited to lower positions in the clause (Postma 1994; Bhat 2000).

(44) Shoshone bare wh indefinites must be in-situ:
a. Hakke in puikka?
b. Ni kianhakke puikka.
who you saw
I perhaps who saw‘Who did you see?’‘I saw someone.’(Bhat 2000, p. 383, citing Miller 1996)

 The distribution of ∃reset may be syntactically restricted.

55

Different syntactic restrictions

One example: In many languages with bare wh indefinites, they are
limited to lower positions in the clause (Postma 1994; Bhat 2000).

(44) Shoshone bare wh indefinites must be in-situ:
a. Hakke in puikka?
b. Ni kianhakke puikka.
who you saw
I perhaps who saw‘Who did you see?’‘I saw someone.’(Bhat 2000, p. 383, citing Miller 1996)

 The distribution of ∃reset may be syntactically restricted.

55

§6 Conclusion

56

Conclusion

Today I introduced a framework for productively understanding
patterns of wh-quantification in two-dimensional Alternative
Semantics.
• A few basic, independently motivated ingredients — wh, J,
A LT S HIFT, ∃, and ∃reset — can together model the behavior ofmany attested forms of wh-quantification.
• Crucial are the roles of Interpretability and reset. Both areassumed notions in previous work, but they hold the key tounderstanding the frequent use of focus particles and disjunctionin wh-quantification.

57

Conclusion

Today I introduced a framework for productively understanding
patterns of wh-quantification in two-dimensional Alternative
Semantics.
• A few basic, independently motivated ingredients — wh, J,
A LT S HIFT, ∃, and ∃reset — can together model the behavior ofmany attested forms of wh-quantification.
• Crucial are the roles of Interpretability and reset. Both areassumed notions in previous work, but they hold the key tounderstanding the frequent use of focus particles and disjunctionin wh-quantification.

57

Conclusion

Today I introduced a framework for productively understanding
patterns of wh-quantification in two-dimensional Alternative
Semantics.
• A few basic, independently motivated ingredients — wh, J,
A LT S HIFT, ∃, and ∃reset — can together model the behavior ofmany attested forms of wh-quantification.
• Crucial are the roles of Interpretability and reset. Both areassumed notions in previous work, but they hold the key tounderstanding the frequent use of focus particles and disjunctionin wh-quantification.

57

Conclusion
Q: Why are focus particles and disjunctors commonly involved in
wh-quantification?
A:

i. Focus particles are unique in the grammar in being able toaltaccess alternative sets (J...K ) (see e.g. Rooth 1992).
(Disjunctive particles often spell out ∃reset .)ii. Focus particles are resetting, and therefore can repair
violations of Interpretability, especially following theapplication of ∃.

The frequent use of focus particles in wh-quantification is
unexplained by earlier approaches to wh-quantification such as
Kratzer and Shimoyama 2002, which proposes various operators thatquantify over alternatives which are unrelated to focus particles.
58

Conclusion
Q: Why are focus particles and disjunctors commonly involved in
wh-quantification?
A:

i. Focus particles are unique in the grammar in being able toaltaccess alternative sets (J...K ) (see e.g. Rooth 1992).
(Disjunctive particles often spell out ∃reset .)ii. Focus particles are resetting, and therefore can repair
violations of Interpretability, especially following theapplication of ∃.

The frequent use of focus particles in wh-quantification is
unexplained by earlier approaches to wh-quantification such as
Kratzer and Shimoyama 2002, which proposes various operators thatquantify over alternatives which are unrelated to focus particles.
58

Conclusion
Q: Why are focus particles and disjunctors commonly involved in
wh-quantification?
A:

i. Focus particles are unique in the grammar in being able toaltaccess alternative sets (J...K ) (see e.g. Rooth 1992).
(Disjunctive particles often spell out ∃reset .)ii. Focus particles are resetting, and therefore can repair
violations of Interpretability, especially following theapplication of ∃.

The frequent use of focus particles in wh-quantification is
unexplained by earlier approaches to wh-quantification such as
Kratzer and Shimoyama 2002, which proposes various operators thatquantify over alternatives which are unrelated to focus particles.
58

Conclusion
Q: Why are focus particles and disjunctors commonly involved in
wh-quantification?
A:

i. Focus particles are unique in the grammar in being able toaltaccess alternative sets (J...K ) (see e.g. Rooth 1992).
(Disjunctive particles often spell out ∃reset .)ii. Focus particles are resetting, and therefore can repair
violations of Interpretability, especially following theapplication of ∃.

The frequent use of focus particles in wh-quantification is
unexplained by earlier approaches to wh-quantification such as
Kratzer and Shimoyama 2002, which proposes various operators thatquantify over alternatives which are unrelated to focus particles.
58Thank you!

Thank you! Questions?
For comments and discussion, I thank Nadine Bade, Rahul Balusu,
Sigrid Beck, Kenyon Branan, Aron Hirsch, Utpal Lahiri, Keely New,and especially Hadas Kotek, and the audiences at the Tokai
Semantics Workshop, the University of Tübingen, and Michigan State
University.

59References I
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Semantics 15:65–94.
Alonso-Ovalle, Luis. 2004. Simplification of disjunctive antecedents. In
Proceedings of NELS 34, ed. Keir Moulton and Matthew Wolf, 1–5.
Amritavalli, R. 2003. Question and negative polarity in the disjunction phrase.
Syntax 6:1–18.
Beck, Sigrid. 2006. Intervention effects follow from focus interpretation.
Natural Language Semantics 14:1–56.
Bhat, Darbhe Narayana Shankara. 2000. The indefinite-interrogative puzzle.
Linguistic Typology 4:365–400.
Chierchia, Gennaro. 2013. Logic in grammar: Polarity, free choice, andintervention. Oxford University Press.
Choi, Jinyoung. 2007. Free choice and negative polarity: a compositional
analysis of Korean polarity sensitive items. Doctoral Dissertation,
University of Pennsylvania.

60References II
Choi, Jinyoung, and Maribel Romero. 2008. Rescuing existential free choiceitems in episodic sentences. In Empirical Issues in Syntax and Semantics
7 , ed. Olivier Bonami and Patricia Cabredo Hofherr, 77–98.
Dawson, Virginia. 2018. Two disjunctions in Tiwa: Morphologicallydifferentiated disjunction scope. Handout.
Dawson, Virginia. 2019. Lexicalizing disjunction scope. In Proceedings of the
LSA, volume 4, 1–13.
Dawson, Virginia. to appear. Tiwa indeterminates and NP restriction in a
Hamblin semantics. In Proceedings of FASAL 7 .
Den Dikken, Marcel. 2006. Either-float and the syntax of co-or-dination.
Natural Language & Linguistic Theory 24:689–749.
Erlewine, Michael Yoshitaka. 2017a. Quantifying over alternatives with Toba
Batak manang. Presented at AFLA 24, Triple A 4.
Erlewine, Michael Yoshitaka. 2017b. Two disjunctions in Mandarin Chinese.
Manuscript, National University of Singapore.

61

References III
Erlewine, Michael Yoshitaka. 2019. Uses of Tibetan yin.n’ang. Presented atthe 2019 Singapore Summer Meeting.
Erlewine, Michael Yoshitaka, and Hadas Kotek. 2016. Even-NPIs in
Dharamsala Tibetan. Linguistic Analysis 40:129–165.
Erlewine, Michael Yoshitaka, and Keely Zuo-Qi New. 2019. A variably
exhaustive and scalar focus particle and pragmatic focus concord in
Burmese. Manuscript, National University of Singapore.
Fox, Danny. 2007. Free choice and the theory of scalar implicatures. In
Presupposition and implicature in compositional semantics, ed. Uli
Sauerland and Penka Stateva, 71–120. Springer.
Giannakidou, Anastasia, and Lisa Lai-Shen Cheng. 2006. (In)definiteness,polarity, and the role of wh-morphology in free choice. Journal of
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Gill, Kook-Hee, Steve Harlow, and George Tsoulas. 2006. Disjunction andindeterminate-based quantification in Korean. Manuscript, University of
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References IV
Hamblin, Charles. 1973. Questions in Montague English. Foundations ofLanguage 10:41–53.
Haspelmath, Martin. 1997. Indefinite pronouns. Oxford.
Heim, Irene. 1984. A note on negative polarity and DE-ness. In Proceedingsof NELS 14, 98–107.
Huang, Cheng-Teh James. 1982. Logical relations in Chinese and the theoryof grammar. Doctoral Dissertation, Massachusetts Institute of Technology.
Kim, Min-Joo, and Stefan Kaufmann. 2006. Domain restriction in freedom of
choice: A view from Korean indet-na items. In Proceedings of Sinn und
Bedeutung 11, 375–389.
Kotek, Hadas. 2016. On the semantics of wh-questions. In Proceedings ofSinn und Bedeutung 20, ed. Nadine Bade, Polina Berezovskaya, andAnthea Schöller, 424–447.
Kotek, Hadas. 2019. Composing questions. MIT Press.
Kotek, Hadas, and Michael Yoshitaka Erlewine. 2019. Wh-indeterminates in
Chuj (Mayan). Canadian Journal of Linguistics 64:62–101.

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References V
Kratzer, Angelika, and Junko Shimoyama. 2002. Indeterminate pronouns: theview from Japanese. In The Proceedings of the Third Tokyo Conferenceon Psycholinguistics (TCP 2002), ed. Yuko Otsuka, 1–25. Tokyo: Hitsuji
Syobo.
Krifka, Manfred. 1994. The semantics and programatics of weak and strong
polarity items in assertions. In Proceedings of SALT 4, 195–219.
Kuroda, Sige-Yuki. 1965. Generative grammatical studies in the Japanese
language. Doctoral Dissertation, Massachusetts Institute of Technology.
Ladusaw, William A. 1979. Polarity sensitivity as inherent scope relations.
Doctoral Dissertation, University of Texas at Austin.
Lahiri, Utpal. 1998. Focus and negative polarity in Hindi. Natural Language
Semantics 6:57–123.
Lee, Young-Suk, and Laurence Horn. 1995. Any as indefinite plus even.
Manuscript, Yale University, May 1995.

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References VI
Miller, Wick R. 1996. Sketch of Shoshone, a Uto-Aztecan language. In
Handbook of north american indians: Languages, ed. Ives Goddard,
693–720. Washington: Smithsonian Institution.
New, Keely, and Michael Yoshitaka Erlewine. 2018. The expression of
exhaustivity and scalarity in Burmese. In Proceedings of SALT 28, ed.
Sireemas Maspong, Brynhildur Stefánsdóttir, Katherine Blake, and Forrest
Davis, 271–288.
Postma, Gertjan. 1994. The indefinite reading of wh. Linguistics in the
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Ramchand, Gillian Catriona. 1997. Questions, polarity and alternative
semantics. In Proceedings of NELS 27 , 383–396. GLSA.
Rooth, Mats. 1985. Association with focus. Doctoral Dissertation, Universityof Massachusetts, Amherst.
Rooth, Mats. 1992. A theory of focus interpretation. Natural Language
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References VII
Rullmann, Hotze. 1996. Two types of negative polarity items. In Proceedingsof NELS 26, 335–350.
Shimoyama, Junko. 1999. Internally headed relative clauses in Japaneseand E-type anaphora. Journal of East Asian Linguistics 8:147–182.
Shimoyama, Junko. 2006. Indeterminate quantification in Japanese. Natural
Language Semantics 14:139–173.
Szabolcsi, Anna. 2015. What do quantifier particles do? Linguistics andPhilosophy 38:159–204.
Velleman, Leah, David Ian Beaver, Emilie Destruel, Dylan Bumford, Edgar
Onea, and Liz Coppock. 2012. It-clefts are IT (inquiry terminating)constructions. In Proceedings of SALT 22, 441–460.
Xiang, Yimei. 2016. Interpreting questions with non-exhaustive answers.
Doctoral Dissertation, Harvard.

66

Appendix A: Burmese wh-ONLY FCI(40) Burmese wh-ONLY FCI:

(Keely New, p.c.)

Nga [bal hin]-beh sar-lo ya-dal.
1
which dish-ONLY eat-C get-REAL‘I can eat any dish.’

I define a “pre-exhaustification” operator P RE E XH which exhaustifies
individual alternatives (see Chierchia 2013; Xiang 2016), leaving theordinary denotation unchanged (45).
(Let E XH and ONLY here negate Innocently Excludable alternatives.)

67

Appendix A: Burmese wh-ONLY FCI

o

o

(45)

a. JP RE E XH αK = JαK
o
n
alt
alt
b. JP RE E XH αK = E XHC = JαKalt (a) : a ∈ JαK(46)

a. J[P RE E XH [3 [∃ [I eat which dish]]]]Ko= J[3 [∃ [I eat which dish]]]K = 3 I eat some dishoaltb. J[P(RE E XH [3 [∃ [I eat)which( dish]]]]K)E XH 3 I eat a,
3 a ∧ ¬3 b,==
E XH 3 I eat b,...
3 b ∧ ¬3 a,...

68

Appendix A: Burmese wh-ONLY FCIONLY applied to (45) results in the free choice inference:o(47) J[ONLY [P RE E XH [3 [∃ [I eat which dish]]]]]K= ¬ (3 a ∧ ¬3 b) ∧ ¬ (3 b ∧ ¬3 a) = 3 a ∧ 3 b
some); 3 I eat some dish(given 3

69

Appendix A: Burmese wh-ONLY FCIWithout P RE E XH, ONLY will (again) result in a triviality, as there are no
Innocently Excludable alternatives.
But (47) predicts the free choice inference to be the at-issue content.
This requires further investigation.

70

Appendix B: Tibetan wh-COP-COND-EVEN FCI(41) Tibetan wh-COP-COND-EVEN FCI:

(Erlewine 2019)

Mo.rang [su yin-na]-yang-laskad.cha bshad-gi-red.
she
who COP-COND-EVEN-DAT speech talk-IMPF-AUX[Pema is very friendly.] ‘She talks to anyone.’First, a syntactic puzzle: wh-yin-na-yang formally is a conditionalclause (with EVEN) but in argument position. See especially thedative case in (41).

71Appendix B: Tibetan wh-COP-COND-EVEN FCI I propose to adopt the Shimoyama 1999 E-type anaphora
approach for (Japanese) head-internal relatives: The clause isadjoined above LF, with the argument position interpreted with an
E-type pronoun.

(48)

a. Literal (41): She talks to [even if it’s who] ⇒b. LF: [even if it’s whoi ], she talks to themi⇒ EVEN( if it’s whoi , she talks to themi )72

Appendix B: Tibetan wh-COP-COND-EVEN FCI(49) LF for (41): EVEN[α if ∃[theyi ’re who], she talks(HABITUAL) tothemi ]oJαK = ∧ if it’s someonei , she talks to themialt
JαK = {∧ if it’s x i , she talks to themi : x human}73

Appendix B: Tibetan wh-COP-COND-EVEN FCIo• EVEN(α) asserts JαK : she talks to everyone (as long as they
exist).
o• Notice that the prejacent JαK asymmetrically entails every
alt
proposition in JαK . The presupposition of EVEN is thus satisfied.
o• In addition, I propose that the assertion of JαK instead of a morealt
specific alternative in JαK yields a conversational implicaturethat ‘someone’ in the conditional clause can be verified bymultiple (all?) individuals. This derives the free choice inference.

74Appendix B: Tibetan wh-COP-COND-EVEN FCI(50)* Episodic LF: EVEN[α if ∃[iti ’s what], he’s eating it i right now ]In this episodic situation, either the speaker knows what specifically is
being eaten right now (maybe multiple things) — and therefore shouldalt
be able to say a more specific alternative in JαK , contra theimplicature above — or they can’t be certain (and therefore shouldn’tosay, by Quality) that everything is being eaten right now (JαK ).

75