Proceedings of SALT 26: xxx-xxx, 2016
Fragment functional answers*
Yael Sharvit
University of California, Los Angeles
Jungmin Kang
University of Connecticut
Abstract An answer to a question may be expressed with a full clause
reply or with a fragment reply. We discuss the fact that some fragment
replies are unacceptable replies to multiple-wh interrogatives, and
suggest that the reason for this is that fragment replies are the basic
semantic answers while full clause replies are sometimes parasitic on
them.
Keywords fragments, functional wh questions, pair-list wh questions
1 Full clause replies or fragments?
The wh interrogative Which student turned in this paper may be answered with
the full clause reply in (1a) or with its fragment in (1b) (here and throughout, a
fragment of a string S is some sub-string of S distinct from S).
(1) Which student turned in this paper?
a. Marv turned in this paper.
b. Marv.
It is a matter of some debate which of these – the full clause reply in (1a) or its
fragment in (1b) – expresses the basic answer. We discuss a puzzle noted in Kang
2012 that challenges the full-clauses-are-basic approach. The puzzle concerns
contrasts between so-called functional replies and so-called pair-list replies to
multiple-wh interrogatives. To illustrate, consider Which student turned in which
paper. It may be answered with the full clause pair-list reply in (2a) as well as
with its fragment in (2b) (as reported in Merchant 2004; though see Jacobson
2016).
* For their invaluable input, we are grateful to Veneeta Dayal, Polly Jacobson, Jason Merchant,
five anonymous SALT26 reviewers, and audiences at UCLA Semantics Tea, Washington
University in St. Louis Linguistics Colloquium and SALT26.
©2016 Sharvit & Kang
Sharvit & Kang
(2) Which student turned in which paper?
a. Marv turned in Binding, Fred turned in Anaphora, (and) Sam turned in
Tense.
b. Marv, Binding; Fred, Anaphora; (and) Sam, Tense.
But while the same interrogative can also be answered with the full clause
“functional” reply in (3a) (see Dayal 1996 and Comorovski 1996), neither the
fragment of (3a) in (3b), nor its fragment in (3c), is a fully well-formed reply (see
Kang 2012): (3c) is considerably degraded, and (3b) is simply unacceptable.
(3) Which student turned in which paper?
a. Every student turned in his term paper.
b. ##His term paper.
c. #Every student, his term paper.
Following Jacobson 2016, we propose that semantic answers are expressed by
fragments and full clause replies can sometimes be parasitic on fragments.
Specifically, regarding Which student turned in which paper, we propose (4).
(4) a. His term paper is not a well-formed reply because its semantic value is a
natural function of type <s, <e, e>> (i.e., an <e, e>-function concept),
while the question seeks a function of type <<s, e>, <s, e>> (i.e., a
function from individual concepts to individual concepts).
b. Marv, Binding; Fred, Anaphora; (and) Sam, Tense, whose semantic value
is a function of type <<s, e>, <s, e>>, is a well-formed reply, as is Marv
turned in Binding, Fred turned in Tense, (and) Sam turned in Anaphora,
which is parasitic on Marv, Binding; Fred, Anaphora; (and) Sam, Tense.
c. Every student turned in his term paper may be a well-formed reply
because it, too, may sometimes be parasitic on Marv, Binding; Fred,
Anaphora; (and) Sam, Tense.
d. The degraded status of Every student, his term paper results from some
additional principles that are pragmatic in nature.
Section 2 spells out what the puzzle illustrated by (2)-(3) is and explains why
we do not pursue an analysis that takes full clauses to express semantic answers.
Section 3 spells out the foundations of the proposal, explaining why (3b) is not a
well-formed reply to Which student turned in which paper while (3a) is. Section 4
presents a pragmatic extension of the proposal, explaining why (3c) is (often) not
a well-formed reply either.
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Fragment functional answers
2 The problem with full clauses as semantic answers
Our contribution to the debate builds on Kang 2012. It concerns the fact that
Every student turned in his term paper is a well-formed reply to the multiple-wh
interrogative Which student turned in which paper (see (3)). Since fragment
replies are available in principle, as shown in (1)-(2), the following puzzle arises
within the approach that says that full clause replies express semantic answers,
and fragment replies are derived from them.
Part I of the puzzle. The fact that Every student turned in his term paper is a
fully well-formed reply to Which student turned in which paper raises the
expectation that its “gapped” fragment Every student, his term paper also be a
fully well-formed reply, yet it is considerably degraded. One might conjecture
that the reason is this: a fragment reply may be formed by deleting parts of the full
clause reply, though gapping (in the sense of Ross 1970), which yields Every
student turned in his term paper, must be avoided. However, while single-pair
gapped fragments are often not well-formed replies (as illustrated by the fact that
Marv, Binding is an odd reply to Which student turned in Binding), there is no
blanket prohibition against gapped fragments, as evidenced by the fact that the
pair-list gapped reply Marv, Binding; Fred, Anaphora; (and) Sam, Tense is a
well-formed reply to Which student turned in which paper, and by the fact that
both the full clause (5a) and its gapped fragment (5b) may be well-formed replies
to this question (in situations where the syntax students and the semantics students
are all the students that there are).
(5) a. Every syntax student turned in his syntax term paper and every semantics
student turned in his semantics term paper.
b. Every syntax student, his syntax term paper; (and) every semantics
student, his semantics term paper.
Part II of the puzzle. The fact that Every student turned in his term paper is a
well-formed reply to Which student turned in which paper raises the expectation
that its noun phrase fragment His term paper also be a well-formed reply. Indeed,
His term paper is a well-formed fragment reply, but to a different question,
namely, Which paper did every student turn in (as observed in, for example,
Engdahl 1986). One might conjecture (following Merchant 2004) that the reason
is the following. A fragment reply may be derived from the full clause reply by
movement of the wh phrase to a clause-initial position – the F(ocus)P(rojection)
position – and by subsequent T(ense)P(rojection)-ellipsis, where the TP in the full
clause reply is elided under identity with the TP in the interrogative. (Ellipsis is
triggered by the E feature – Ellipsis feature – in C(omplementizer).) Accordingly,
since TP in (6b) is identical to TP in (6a) but TP in (6c) is not, and since TP in
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(7c) is identical to TP in (7a) but TP in (7b) is not, Marv, Binding; Fred,
Anaphora; (and) Sam, Tense is a well-formed reply only to Which student turned
in which paper, and His term paper is a well-formed reply only to Which paper
did every student turn in.
(6) a. [CP which student1 which paper2 [TP t1 turned in t2]]
b. [FP Marv1 Binding2 [CP … C[+E] … [TP t1 turned in t2]]] [FP Bill1 Anaphora2
[CP … C[E] … [TP t1 turned in t2]]] …
c. *[FP his term paper2 [CP … C[+E] … [TP every student turned in t2]]]
(7) a. [CP which paper2 [TP every student turned in t2]]
b. *[FP Marv1 Binding2 [CP … C[+E] … [TP t1 turned in t2]]] [FP Bill1
Anaphora2 [CP … C[E] … [TP t1 turned in t2]]] …
c. [FP his term paper2 [CP … C[+E] …[TP every student turned in t2]]]
However, TP in (8) is identical to TP in (6a), in the same way that TP in (6b) is
identical to TP in (6a), with the result that Every student, his term paper should be
a fully acceptable reply, contrary to fact (see Part I of the puzzle).
(8) [FP every student1 his term paper2 [CP … C[+E] … [TP t1 turned in t2]]]
In view of this, we attempt an analysis in the spirit of Jacobson 2016 (cf.
Groenendijk & Stokhof 1984 and Ginzburg & Sag 2000), according to which
semantic answers are expressed by fragments, not full clauses.
3 Wh questions and their semantic answers
Our basic proposal consists of two parts: (i) the semantics of wh interrogatives,
discussed in 3.1; and (ii) the distinction between natural function wh
interrogatives and pair-list wh interrogatives, discussed in 3.2.
3.1 The semantics of wh interrogatives
Theories of questions along the lines of Jacobson 2016 take the intension of a wh
interrogative clause to be a property. For example, the function in (9a), of type <s,
<e, t>>, may be the question-intension of the single-wh interrogative Which
student turned in Binding; this is based on the assumption (see (9b)) that which
student contributes to the meaning a function of type <s, <e, t>>. (9a) may serve
as an argument of a question-embedding verb (such as know or wonder).1
1
[λx: φ. ϕ] is the smallest function ƒ that meets the description in (i) or in (ii), whichever makes
sense (see Heim & Kratzer 1998):
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Fragment functional answers
(9) a. λw: w ∈ W. [[which student [? [turned in Binding]] ]]w =
λw: w ∈ W. λx: x ∈ De & x ∈ STUDENTw. TURN-INw(x, b)
b. For any w ∈ W:
[[Binding]]w = b (where b ∈ De)
[[which student]]w = λx: x ∈ De. x ∈ STUDENTw
According to Jacobson 2016, a matrix interrogative forms a syntactic unit with its
possible (fragment) reply. Since the extension of Marv is m (an element of De),
[Q-A [Which student turned in Binding] [Marv]] is a well-formed syntactic unit
denoting a possible question-answer pair, relative to a world in which m is a
student. The full clause reply Marv turned in Binding may be parasitic on the
fragment reply Marv.
We depart from Jacobson 2016 in two ways: (i) we assume that a wh phrase
such as which student always contributes to the meaning a property of natural
functions, and (ii) we assume that an interrogative and its possible reply are
distinct syntactic units related pragmatically by discourse principles of questionanswer congruence.
Accordingly, the intension of the single-wh interrogative Which student turned
in Binding is the property of natural functions in (10a) (and not the property of
individuals in (9a)). The question-intension in (10a) may serve as an argument of
a question-embedding verb (such as know or wonder). C is the set of possible
utterance contexts, NATc is the set of natural functions salient in c (for any c ∈ C),
and f is restricted to be a student-valued natural function of type <s, e> that is an
element of NATc.2
(10) For any c ∈ C:
a. λw ∈ W. [[which student [? [turned in Binding]] ]]c,w =
λw ∈ W. λf ∈ D<s,e>: f ∈ NATc & Ran(f) ⊆ STUDENTw. TURN-INw(f(w), b)
b. For any w ∈ W:
[[Binding]]c,w = b (where b ∈ De)
[[which student]]c,w = λf ∈ D<s,e>. f ∈ NATc & Ran(f) ⊆ STUDENTw
Since the assumption that wh question-intensions are properties of natural
functions is central to our proposal, let us briefly elaborate on the distinction
(i) ƒ maps every x such that φ to ϕ.
(ii) ƒ maps every x such that φ to True if ϕ, and to False otherwise.
Dσ is the set of semantic objects of type σ and W is the set of possible worlds.
2
The function in (10a) should also be restricted to worlds w and functions f such that w is in the
domain of f. We often omit such definedness conditions (to save space).
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between natural functions and (possibly random) sets of ordered pairs. An
informal characterization of this distinction is given in Jacobson 1999 (Fn. 23):
‘The term “natural function” is perhaps not the most felicitous one
– a better one would be a “procedurally defined function”. I will
not attempt to precisely pin this down here … but the basic
intuition is fairly obvious. A procedurally defined function is an
intensional one: its value can be computed for any new individual
added to the world … A random list of ordered pairs – while
extensionally equivalent to a procedurally defined function for a
given domain – is not a recipe in the same sense.’
We rely on this intuitive understanding of what a natural function is, and do not
attempt to provide a more rigorous or precise definition. We take the distinction
between natural functions and (possibly random) sets of ordered pairs – which we
call ‘pair-lists’ – to be grammatically significant.
Natural functions are typically denoted by definite noun phrases such as the
term paper or his term paper. Pair-lists are typically denoted by strings of pairs
such as Marv, Binding; Fred, Anaphora; (and) Sam, Tense. For example (and in
the spirit of Jacobson 1999), we assume that the basic denotations of his and his
term paper are as in (11); accordingly, his term paper denotes a natural function
in D<s,<e,e>>. We also assume that names are ambiguous; they denote individuals or
functions from worlds to individuals, as illustrated in (12); accordingly, strings of
name-name pairs are also ambiguous, as illustrated in (13).
(11) For any c ∈ C and w ∈ W:
a. [[his]]c,w = λP ∈ D<s,<e,t>>. λw ∈ W. λx ∈ De: x has in w exactly one z such
that P(w)(z) = True. the z such that P(w)(z) = True and x has z in w.
b. [[his term paper]]c,w = [[his]]c,w(λw ∈ W. [[term paper]]c,w) = TRMPPR (=
λw ∈ W. λx ∈ De: x has exactly one term paper in w. the term paper that
x has in w)
(12) For any c ∈ C and w ∈ W: [[Marv]]c,w = m (where m ∈ De)
[[Marv]]c,w = M (where M = λw ∈ W. [[Marv]]c,w)
(13) For any c ∈ C and w ∈ W:
a. [[Marv,Binding;Fred,Anaphora;(and)Sam,Tense]]c,w = {<M, B>, <F,
A>, <S, T>}, which is a (possibly random) list of ordered pairs (an
element of D<<s,e>,<s,e>>)
b. [[Marv, Binding; Fred, Anaphora; (and) Sam, Tense]]c,w = {<m, B>, <f,
A>, <s, T>}, which is a (possibly random) list of ordered pairs (an
element of D<e,<s,e>>)
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Fragment functional answers
While M, B, F, etc. are themselves natural functions, both functions in (13) are
pair-lists.
Returning to interrogatives, we assume (with Krifka (2001) and others) that a
matrix interrogative is embedded under the silent question-act operator ASK, as
illustrated in (14) for Which student turned in Binding, whose intension is (10a).
We also assume that a reply is embedded under the silent answer-act operator
ANS, as shown in (15). For any c ∈ C, wc is the world of c and uc the speaker of c.
(14) λc ∈ C. ASKwc(uc, λw ∈ W. [[which student [? [turned in Binding]] ]]c,w)
(15) λc ∈ C. ANSwc(uc, M)
Interrogatives and their possible replies are subject to various principles of
congruence (see, for example, Roberts 2012). Let us assume that one of those
principles says that for any g, question-intension Q, and utterance context c, <Q,
g> is congruent relative to c+Q (c “updated” with Q) only if for all w ∈ csc+Q, g is
in the domain of Q(w) (where for any c ∈ C, csc is the context set of c in the sense
of Stalnaker 1978 – the conjunction of the beliefs shared by the participants in c).
Accordingly, <(10a), M> may be congruent: M – a natural function of type <s, e>
(see (12)) – is a possible semantic answer to (10a). Therefore, Marv – which
denotes M – may be a well-formed reply to the interrogative Which student
turned in Binding.
This view might raise the following concern. It implies that in a situation
where only m turned in b, Which students turned in Binding may be answered
with The tallest student and the hippest student, provided that m is taller than all
the other students and hipper than all the other students. This may seem counterintuitive. There are, however, situations that suggest otherwise. For example, if
we are trying to determine whether students’ interests affect their timeliness, The
syntax student and the semantics student seems a felicitous reply to Which
students turned in their paper on time, even if m qualifies as both the syntax
student and the semantics student. We therefore maintain the hypothesis that an
interrogative wh phrase quantifies over natural functions, and assume that
independent principles of relevance and salience determine which natural
functions are legitimate possible answers.
The claim that the natural function / pair-list distinction is grammatically
significant receives independent support from the contrast between wh gaps and
resumptive pronouns in Modern Hebrew (as described in Sharvit 1999a in
response to Doron 1982). To illustrate, in (18a,b) kol gever (= ‘every man’) may
be interpreted as having main clause scope, despite the fact that it is within a
scope island (a relative clause) on the surface. Crucially, when (18a) is uttered
right after (16), it implies that for each man x, x’s mother-in-law is x’s number
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one enemy, and when it is uttered right after (17), it implies that Mira is Dan’s
number one enemy, Sarah is David’s and Rina is Ram’s (OM stands for ‘object
marker’). On the other hand, (18b) – with the resumptive pronoun ota (= ‘her’) in
the relative clause – can only imply, when uttered right after (16), that for each
man x, x’s mother-in-law is x’s number one enemy. When it is uttered right after
(17) the discourse is somewhat incoherent.
(16) kol
gever sone et
xamot-o
every man hates OM mother-in-law-his
‘Every man hates his mother-in-law’
(17) dan sone et mira, david son et sara, ve ram sone et rina
Dan hates OM Mira, David hates OM Sarah, and Ram hates OM Rina
‘Dan hates Mira, David hates Sarah, and Ram hates Rina’
(18) a. ha-i∫a
∫e
the-woman that
hi ha-oyevet
is the-enemy
b. ha-i∫a
∫e
the-woman that
hi ha-oyevet
is the-enemy
kol
gever sone
every man hates
mispar
number
exad
one
∫elo
his
kol
gever sone ota
every man hates her
mispar
number
exad
one
∫elo
his
The reason seems to be the following: (16) introduces a natural function (from
men to the women they hate) and (17) introduces a pair-list. The subject noun
phrase in (18a) may be anaphorically related to (16), “picking up” the natural
function introduced in (16) as its referent (along the lines of Jacobson 1994), and
may also be anaphorically related to (17), “picking up” the pair-list introduced in
(17) as its referent (along the lines of Sharvit 1999a,b). But the subject noun
phrase in (18b) – with a resumptive pronoun instead of a gap – may only be
anaphorically related to (16), because a pronoun may denote an individual or a
natural function, but not a pair-list.
3.2 Natural function vs. pair-list questions
That the grammar of natural language is indeed sensitive to the natural function /
pair-list distinction is further corroborated by the fact that some wh interrogatives
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Fragment functional answers
(e.g., single-wh interrogatives with every N in subject position) have a natural
function reading as well as a pair-list reading, while others (e.g., single-wh
interrogatives with no N in subject position) have a natural function reading but
no pair-list reading, and multiple-wh questions have a pair-list reading but no
natural function reading. We discuss the principles that govern the distribution of
these readings borrowing insights from Engdahl 1986, Chierchia 1993, Krifka
2001 and Dayal 1996, 2002 and others (with the adjustments needed to comply
with the assumptions introduced in 3.1).
3.2.1 Single-wh interrogatives with quantificational subject noun phrases
As shown in (19)-(21), the interrogative clauses Which paper did every student
turn in, Which paper did no student turn in and Which paper did most students
turn in all have a “non-co-varying” reading, as evidenced by their well-formed
fragment reply A1, as well as at least one “co-varying” reading, as evidenced by
their well-formed fragment reply A2. The A1 reply does not associate different
students with different papers; the A2 reply may associate different students with
different papers.
(19) Q: Which paper did every student turn in?
A1: Binding.
A2: His term paper.
(20) Q: Which paper did no student turn in?
A1: Binding.
A2: His term paper.
(21) Q: Which paper did most students turn in?
A1: Binding.
A2: Their term paper.
It follows from the assumptions in 3.1 that the grammar generates a “non-covarying” meaning for each of these interrogatives, as follows.
(22) a. λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<s,e>: f ∈ NATc & Ran(f) ⊆
ALL y [y ∈ STUDENTw] [TURN-INw(y, f(w))])
b. λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<s,e>: f ∈ NATc & Ran(f) ⊆
NO y [y ∈ STUDENTw] [TURN-INw(y, f(w))])
c. λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<s,e>: f ∈ NATc & Ran(f) ⊆
MOST y [y ∈ STUDENTw] [TURN-INw(y, f(w))])
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PAPERw.
PAPERw.
PAPERw.
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Since the denotation of Binding is B, which is a natural function of type <s, e>
(see (12)-(13)), Binding is a possible well-formed “non-co-varying” reply to the
interrogatives in (19)-(21) (provided all other congruence principles are obeyed).
(23) λc ∈ C. ANSwc(uc, B)
In the spirit of Engdahl 1986 and Chierchia 1993, and Groenendijk & Stokhof
1984, we assume that each of these interrogatives may also receive a “co-varying”
interpretation, denoting a property of paper-valued natural functions of type <s,
<e, e>>, where the quantificational subject binds a variable in the complex
“functional” gap/trace of the wh phrase.
(24) a. λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<s,<e,e>>: f ∈ NATc & Ran(f(w)) ⊆
PAPERw. ALL y [y ∈ STUDENTw] [TURN-INw(y, f(w)(y))])
b. λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<s,<e,e>>: f ∈ NATc & Ran(f(w)) ⊆
PAPERw. NO y [y ∈ STUDENTw] [TURN-INw(y, f(w)(y))])
c. λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<s,<e,e>>: f ∈ NATc & Ran(f(w)) ⊆
PAPERw. MOST y [y ∈ STUDENTw] [TURN-INw(y, f(w)(y))])
Since the basic denotation of his/their term paper is TRMPPR, which is a natural
function of type <s, <e, e>> (see (11)), his/their term paper is a possible wellformed “co-varying” natural function reply to the interrogatives in (19)-(21)
(provided all other relevant congruence principles are obeyed).3
(25) λc ∈ C. ANSwc(uc, TRMPPR)
As is well known, of these interrogatives only Which paper did every student
turn in has a “co-varying” pair-list reading in addition to its “co-varying” natural
function reading (see Engdahl 1986, Chierchia 1993, Groenendijk & Stokhof
1984). This is illustrated by (26)-(28): Which paper did every student turn in may
be answered with the fragment reply A3, but the other two questions cannot be
answered with similar fragment replies.
(26) Q: Which paper did every student turn in?
A3: Marv, Binding; Fred, Anaphora; (and) Sam, Tense.
3
It is, of course, conceivable that the “non-co-varying” meaning of each of the interrogatives in
(19)-(21) is a special case of its <s, <e, e>>-meaning. Still, the assumption that the grammar
generates the extra meanings in (22) is harmless.
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Fragment functional answers
(27) Q: Which paper did no student turn in?
A3: #Marv, Binding; Fred, Anaphora; (and) Sam, Tense.
(28) Q: Which paper did most students turn in?
A3’: #Marv, Binding; (and) Fred, Anaphora.
Following Krifka 2001, we assume that the pair-list reading of Which paper did
every student turn in is derived by quantifying every student into the question act,
as shown in (29), where every student z in wc is mapped to the question-intension
of Which paper did z turn in.
(29) λc ∈ C. ALL z [z ∈ STUDENTwc] [ASKwc(uc, λw ∈ W. λf ∈ D<s,e>: f ∈ NATc &
Ran(f) ⊆ PAPERw. TURN-INw(z, f(w)))]
We assume that STUDENTwc = {x ∈ De| for all w ∈ csc: x ∈ STUDENTw} and we
refer to [λz ∈ STUDENTwc. λw ∈ W. λf ∈ D<s,e>: f ∈ NATc & Ran(f) ⊆ PAPERw.
TURN-INw(z, f(w)))] as a family of question-intensions. Let us revise our notion of
question-answer congruence as follows: <Q, g> is congruent relative to c+Q only
if either (i) or (ii) holds: (i) Q is a question-intension and for all w ∈ csc+Q, g is in
the domain of Q(w); (ii) Q is a family of question-intensions and g is the smallest
h such that for every z in the domain of Q, <Q(z), h(z)> is, by (i), congruent
relative to c+Q(z). Since the denotation of Marv, Binding; Fred, Anaphora; (and)
Sam, Tense is the pair-list {<m, B>, <f, A>, <s, T>}, of type <e, <s, e>> (see
(13b)), it is correctly predicted, by (ii), to be a possible well-formed reply to
Which paper did every student turn in, on its reading in (29), provided that
STUDENTwc = {m, f, s}.
(30) λc ∈ C. ANSwc(uc, {<m, B>, <f, A>, <s, T>})
Importantly, His term paper is never a well-formed reply to the pair-list
reading of Which paper did every student turn in. The basic meaning of his term
paper is in D<s,<e,e>>, and it has two derived meanings: for any w ∈ W and any x ∈
De, [[ˇ[his term paper] ]]c,w (= [[his term paper]]c,w(w), which is in D<e,e>) and [[ˇ[his
term paper] ]]c,w(x) (which is in De). Given the meaning of his in (11a), no other
derived meanings are available for his term paper. In particular, it cannot have a
meaning of type <e, <s, e>> (the type of {<m, B>, <f, A>, <s, T>}), as might be
the case under some variants of Heim & Kratzer 1998, according to which he is a
variable of type e with an index that may be abstracted over, as in (31).
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(31) For any c ∈ C, w ∈ W and variable assignment g:
[[3 ˆ[he3’s term paper] ]]c,w,g =
[λx ∈ De. λw ∈ W: [[he3’s term paper]]c,w,g[3àx] is defined. [[he3’s term
paper]]c,w,g[3àx]] =
[λx ∈ De. λw ∈ W: x has a unique term paper in w. x’s term paper in w]
Crucially, the meaning in (31) is not derivable in our system.
According to Krifka (2001), quantification into the question act / speech act is,
in general, possible with every but not with no or most, as illustrated in (32)-(33):
(32a) is a well-formed baptism but (32b,c) are not; (33a) has a description reading
as well as a curse reading but (33b,c) only have a description reading.
(32) a. I hereby baptize every one of you John.
b. #I hereby baptize none of you John.
c. #I hereby baptize most of you John.
(33) a. Every one of you is a crook. / Every one of you is a crook!
b. None of you are crooks. / #None of you are crooks!
c. Most of you are crooks. / #Most of you are crooks!
This, suggests Krifka, follows from more general principles that have to do with
properties unique to universal determiners (as described in Keenan and Faltz
1985). The contrast illustrated by (26)-(28) is therefore predicted.
3.2.2 Multiple-wh interrogatives and their replies
A multiple-wh interrogative such as Which student turned in which paper
intuitively seeks a reply that pairs every student with the paper he turned in (see
Baker 1970 and others). On Dayal’s (1996, 2002) analysis, the question denoted
by that interrogative seeks a pair-list, with the first wh phrase determining the
domain of the list as the set of students, and the second wh phrase determining the
range as a set of papers. In the current system, the question seeks a slightly
different pair-list since, by assumption, each wh phrase contributes a property of
natural functions. Accordingly, the first wh phrase determines the domain of the
pair-list as the set of salient student-valued natural <s, e>-functions, and the
second wh phrase determines the range as a set of paper-valued natural <s, e>functions.
(34) λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<<s,e>,<s,e>>: Dom(f) = {h ∈ D<s,e>| h ∈
NATc & Ran(h) ⊆ STUDENTw} & Ran(f) ⊆ {h ∈ D<s,e>| h ∈ NATc & Ran(h) ⊆
PAPERw}. ALL g [g ∈ Dom(f)] [TURN-INw(g(w), f(g)(w))])
12
Fragment functional answers
Since the denotation of Marv,Binding;Fred,Anaphora;(and)Sam,Tense is the
pair-list {<M, B>, <F, A>, <S, T>}, of type <<s, e>, <s, e>> (see (13a)), it is
correctly predicted to be a possible well-formed reply to Which student turned in
which paper, provided all relevant congruence principles are obeyed. We assume
that {M, F, S} is a set of student-valued <s, e>-members of NATc only if {m, f, s}
is the set of students in the worlds of csc.
(35) λc ∈ C. ANSwc(uc, {<M, B>, <F, A>, <S, T>})
As illustrated by (3b) above, the natural function expression his term paper is
not a well-formed reply to Which student turned in which paper. The reason is
this: by assumption, the denotation of his term paper is of type <s, <e, e>>, while
the question seeks a function of type <<s, e>, <s, e>>. Crucially, given the
meaning of his in (11a), his term paper cannot have a meaning of type <<s, e>,
<s, e>>, basic or derived. In Dayal’s system, on the other hand, Which student
turned in which paper may seek an answer of type <e, e>. If we followed Dayal
and didn’t restrict wh phrases to natural functions, we would not exclude his term
paper as a reply, because <e, e> is one of its derived types.
In addition, if the student’s term paper denoted the natural function [λw ∈ W.
λf ∈ D<s, e>: f(w) is a student in w and there is a unique y such that y is f(w)’s
term-paper in w. [λw’ ∈ W. the unique y such that y is the term paper of f(w) in
w]] (instead of [λw ∈ W: there is a unique student in w and that student has a
unique term paper in w. the student’s unique term paper in w]), it would
sometimes qualify as a well-formed reply to Which student turned in which paper
(as its derived type would be <<s, e>, <s, e>>).4
The table in (36) illustrates the predictions made so far: a single-wh
interrogative with a quantificational subject has a “co-varying” natural function
reading; a single-wh interrogative with a universal quantificational subject has a
“co-varying” pair-list reading, as does a multiple-wh interrogative. A multiple-wh
interrogative does not have a natural function reading; a single-wh interrogative
whose subject is not a universal quantifier does not have a pair-list reading.
4
There is, of course, a noun phrase that does denote that function (that element of D<s,<<s,e>,<s,e>>>
such that … ). It cannot be a reply to the interrogative we are considering for the same reason that
element of De that is my syntax paper cannot be a reply to Which paper did you turn in (while my
syntax paper can).
13
Sharvit & Kang
(36)
“Co-varying”
Interrogative
natural function reply
a. Which paper did
his term paper
every student turn in? <s, <e, e>>, (24a)
b. Which paper did
no student turn in?
c. Which student turned
in which paper?
his term paper
<s, <e, e>>, (24b)
N/A
“Co-varying”
pair-list reply______
Marv, Binding; Fred,
Anaphora …
<e, <s, e>>, (29)
N/A
Marv, Binding; Fred,
Anaphora …
<<s, e>, <s, e>>, (34)
Usually, a full clause reply is available only when the corresponding fragment
is. But as we saw in Section 2, Every student turned in his term paper is a wellformed reply to Which student turned in which paper, despite the fact that his
term paper is not (see (36c)). For space limitations, we present the reason for this
in very rough and sketchy terms.
Let Q, g and c be such that <Q, g> is congruent relative to c+Q. For any
clause S and any α such that for all w ∈ W, g = [[α]]c,w, S is parasitic on α relative
to c+Q only if (i) or (ii) or (iii) holds: (i) Q is a question-intension and for all w ∈
csc+Q, [[S]]c,w = Q(w)(g); (ii) Q is a family of question-intensions and for all w ∈
csc+Q, [[S]]c,w = ∩{p| there is a z in the domain of Q such that p = [λw’ ∈ W.
Q(z)(w’)(g(z))]}(w); (iii) there is a S’ which is parasitic on α relative to c+Q, and
for all w ∈ csc+Q, [[S’]]c,w = [[S]]c,w. Accordingly, the following is predicted.
(37) a. Marv turned in Binding may, by (i), be parasitic on Marv replying to
Which student turned in Binding (see (10a)).
b. Every student turned in his term paper may, by (i), be parasitic on his
term paper replying to Which paper did every student turn in (see (24a)).
c. No student turned in his term paper may, by (i), be parasitic on his term
paper replying to Which paper did no student turn in (see (24b)).
d. Marv turned in Binding, Fred turned in Anaphora (and) Sam turned in
Tense may, by (i), be parasitic on Marv,Binding;Fred,Anaphora;(and)
Sam, Tense replying to Which student turned in which paper (see (34))
and, by (ii), on Marv, Binding; Fred, Anaphora; (and) Sam, Tense
replying to Which paper did every student turn in (see (29)).
e. Every student turned in his term paper may, by (iii), be parasitic on
Marv, Binding; Fred, Anaphora; (and) Sam, Tense replying to Which
student turned in which paper (see (34)) and on Marv, Binding; Fred,
14
Fragment functional answers
Anaphora;(and) Sam,Tense replying to Which paper did every student
turn in (see (29)).
Notice that there is no expression that Marv didn’t turn in Binding, Fred didn’t
turn in Anaphora (and) Sam didn’t turn in Tense can be parasitic on as a reply to
Which paper did no student turn in.
As we saw in Section 1, the gapped fragment Every student, his term paper is
not a fully well-formed reply to Which student turned in which paper. Indeed,
there is no source for such a fragment reply in the system described in Section 3
(see (36)). However, as we saw in Section 2, some alternative gapped fragment
replies to this question are well-formed. We now sort out these facts.
4 Higher order pair-list questions
Consider the single-wh interrogative Which paper did Marv turn in, with the
name Marv in subject position. It may be answered with Binding and with Marv
turned in Binding, but the gapped reply Marv, Binding is a considerably degraded
reply. The first two facts are predicted by the proposal in Section 3: Binding
denotes a possible semantic answer to the question in (38); and Marv turned in
Binding is a full clause reply that may be parasitic on Binding.
(38) λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<s,e>: f ∈ NATc & Ran(f) ⊆ PAPERw. TURNINw(m, f(w)))
The third fact, however, does not follow from anything so far, because nothing so
far rules out (39) – where Marv is quantified into the question-act – as a possible
interpretation of Which paper did Marv turn in (cf. Which paper did every student
turn in, interpreted as in (29)).
(39) λc ∈ C. ALL z [z ∈ {m}] [ASKwc(uc, λw ∈ W. λf ∈ D<s,e>: f ∈
Ran(f) ⊆ PAPERw. TURN-INw(z, f(w)))]
NATc
&
We propose that a pragmatic principle – Avoid Singleton Lists – disfavors a
question that seeks a function with a singleton domain, or a question that seeks a
singleton family of answers, whenever there is an alternative way to seek the
same information that doesn’t “involve” a function with a singleton domain.
Accordingly, (38) is favored over (39).
Now consider again the multiple-wh interrogative Which student turned in
which paper. Every student, his term paper is a degraded reply, compared to
Marv,Binding;Fred,Anaphora;(and)Sam,Tense (and to Every student turned in
15
Sharvit & Kang
his term paper, which may be parasitic on Marv,Binding;Fred,Anaphora;(and)
Sam,Tense). Interestingly, the gapped reply in (40a) may be a fully well-formed
reply (as is its full clause counterpart in (40b)), in situations where the syntax
students and the semantics students are all the students that there are.
(40) a. Every syntax student, his syntax term paper; and every semantics student,
his semantics term paper.
b. Every syntax student turned in his syntax term paper; and every
semantics student turned in his semantics term paper.
We account for this as follows. Which student turned in which paper has a higher
order Dayal-style interpretation (in addition to its interpretation in (34)), which in
principle may have both (40a) and Every student, his term paper as fragment
replies, but the latter is ruled out by Avoid Singleton Lists.
The higher order interpretation of Which student turned in which paper is
given in (41). PARTc(λw ∈ W. [[student]]c,w) is a variable whose value is the set of
c-relevant quantifier intensions of the form [λw ∈ W. [[every]]c,w(Z)] such that Z is
a subset of the set of students, and the union of all the Zs represented in
PARTc(λw ∈ W. [[student]]c,w) is the set of all students (see (42)).5
(41) λc ∈ C. ASKwc(uc, λw ∈ W. λf ∈ D<<s,<<e,t>,t>>,<s,<e,e>>>: Dom(f) =
{h ∈ D<s,<<e,t>,t>>| h ∈ NATc & h ∈ PARTc(λw’ ∈ W. [[student]]c,w’)} &
Ran(f) ⊆ {h ∈ D<s,<e,e>>| h ∈ NATc & Ran(h(w)) ⊆ PAPERw}.
ALL g [g ∈ Dom(f)] [g(w)(λz ∈ De. TURN-INw(z, f(g)(w)(z))) = True])
(42) For any c ∈ C and P ∈ D<s,<e,t>>, PARTc(P) is some non-empty subset of
D<s,<<e,t>,t>> such that:
(i) for all P’ ∈ PARTc(P), there is an expression – αP’ – such that: (a) P’ =
[λw ∈ W. [[every αP’]]c,w], and (b) for all w ∈ W, {x ∈ De| [[αP’]]c,w(x) =
True} ⊆ {x ∈ De| P(w)(x) = True}; and
(ii) for all w ∈ csc, {x ∈ De| P(w)(x) = True} = U{Z| there is a P’ ∈
PARTc(P) such that {x ∈ De| [[αP’]]c,w(x) = True} = Z}.
When PARTc(λw ∈ W. [[student]]c,w) = {[λw ∈ W. [[every syntax student]]c,w], [λw
∈ W. [[every semantics student]]c,w]}, the pair-list {<[λw ∈ W. [[every syntax
student]]c,w], SNTX-TRMPPR>, <[λw ∈ W. [[every semantics student]]c,w],
SMNTCS-TRMPPR>} is a possible semantic answer to (41). When PARTc(λw
5
This is a first approximation. The definition of ‘PART’ will ultimately have to rule in “mixed”
replies such as Every syntax student, his syntax paper; most semantics students, their semantics
paper; some phonetics students, their phonology paper; and the rest, their personal statement.
16
Fragment functional answers
∈ W. [[student]]c,w) = {[λw ∈ W. [[every student]]c,w]}, the single-pair {<[λw ∈ W.
[[every student]]c,w], TRMPPR>} is a possible semantic answer to (41), but it
violates Avoid Singleton Lists: the same information can be obtained, for
example, from (24a), with His term paper as a fragment reply. Therefore, Every
student, his term paper is usually not a well-formed reply to Which student turned
in which paper. For space limitations, we do not discuss the circumstances in
which Avoid Singleton Lists may be overridden.
In a similar fashion, the single-wh interrogative Which paper did every student
turn in has a higher order Krifka-style interpretation (in addition to its
interpretation in (29)), as suggested by the fact that the fragment reply in (40a) is
a well-formed reply to it (as is its full clause counterpart in (40b)), whenever the
syntax students and the semantics students are all the students that there are.
(43) λc ∈ C. ALL g [g ∈ PARTc(λw ∈ W. [[student]]c,w)] [ASKwc(uc, λw ∈ W. λf
∈ D<s,<e,e>>: f ∈ NATc & Ran(f(w)) ⊆ PAPERw. g(w)(λz ∈ De. TURN-INw(z,
f(w)(z))) = True)]
When PARTc(λw ∈ W. [[student]]c,w) = {[λw ∈ W. [[every syntax student]]c,w], [λw
∈ W. [[every semantics student]]c,w]}, the pair-list {<[λw ∈ W. [[every syntax
student]]c,w], SNTX-TRMPPR>, <[λw ∈ W. [[every semantics student]]c,w],
SMNTCS-TRMPPR>} is a possible family of semantic answers. When
PARTc(λw ∈ W. [[student]]c,w) = {[λw ∈ W. [[every student]]c,w]}, the single-pair
{<[λw ∈ W. [[every student]]c,w], TRMPPR>} is a possible family of semantic
answers, but it violates Avoid Singleton Lists.
The higher order analysis of pair-list wh interrogatives is independently –
though indirectly – motivated by quantificational variability effects (in the sense
of Berman 1991 and Lahiri 1991). Note the similarity between the higher order
analysis of pair-list wh interrogatives and the analysis of quantificational
variability effects in Beck & Sharvit 2002: for any question-intension Q and c ∈
C, PARTc(Q) is defined as the set of c-relevant sub-questions of Q; it restricts the
domain of quantification of the adverb that modifies the sentence in which the
interrogative that denotes Q is embedded, as illustrated in (44).
(44) a. John knows, for the most part, which students passed the exam.
b. Intuitive meaning of (44a), roughly:
For most students x, John knows whether x passed the exam.
c. Interpretation of (44a) in the style of Beck & Sharvit 2002:
λc ∈ C. MOST Q [Q ∈ PARTc(λw ∈ W. [[which students passed the
exam]]c,w)] [KNOWwc(j, Q)]
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Sharvit & Kang
By (44c), the meaning of (44a) paraphrased in (44b) may come about in some
utterance context c where PARTc(λw ∈ W. [[which students passed the exam]]c,w)
= {Did m pass the exam?, Did f pass the exam?, Did s pass the exam?, Did a pass
the exam?} and {m, f, s, a} is the set of students in the worlds of csc.
5 Open questions
In the literature, arguments favoring the view that full clause replies are basic
usually rely on morpho-syntactic effects (e.g., Morgan 1973). For example, the
fact that himself, but not him, is a well-formed reply to Who did John shave, on
the reading that implies SHAVE(j, j), is easily accounted for if himself is derived
from the full clause reply John shaved himself, and him is derived from the full
clause reply John shaved him. The reason is that John shaved himself complies
with Binding Theory (Chomsky 1981) when John and the reflexive pronoun
himself corefer, but John shaved him violates Condition B of Binding Theory
when John and the non-reflexive pronoun him corefer. On the other hand,
arguments favoring the view that fragment replies are basic usually rely on
semantic/pragmatic contrasts between full clause replies and fragment replies (see
Jacobson 2016). For example, the fact that Claribel and Enzo were awarded
prizes is a somewhat odd reply to Which students who had come to the party
without costumes were awarded prizes, while the corresponding noun phrase
fragment is felicitous, suggests that the “real” semantic answer is the fragment.
The problem with Claribel and Enzo were awarded prizes might be that it does
not entail/presuppose that c and e had come to the party without costumes, while
the interrogative itself “ignores” anyone who hadn’t.
A comprehensive comparison between the full-clause-replies-are-basic
approach and the fragments-are-basic approach is beyond the scope of this paper,
whose main purpose is to add to the debate the challenge posed by multiple-wh
interrogatives. For space limitations, many challenges faced exclusively by the
fragments-are-basic approach are not addressed here. One of those challenges is
the status of fragment replies vs. full clause replies to multiple-wh interrogatives
in which one of the wh phrases is in a syntactic island (e.g., Which committee
member wants to hire someone who speaks which language, discussed in
Merchant 2004). What makes this problem so difficult to address is the lack of
agreement among speakers (and among question scholars) regarding the
grammatical status of such interrogatives (and their replies) and their relationship
to so-called single-pair questions and echo-questions (for discussion, see Dayal
1996, 2002, 2016, Kotek 2014 and references cited there).
18
Fragment functional answers
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Yael Sharvit
UCLA Linguistics
3125 Campbell Hall
Los Angeles, CA 90095-1543
[email protected]
Jungmin Kang
UConn Linguistics
365 Fairfield Way
Storrs, CT 06269-1145
[email protected]
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