Questions are Immediate Issues

Questions are Immediate Issues
Yurie Hara
Department of Linguistics and Translation
City University of Hong Kong
83, Tat Chee Avenue
Kowloon, Hong Kong SAR
y.hara@cityu.edu.hk
May 14, 2015
Abstract
There is an asymmetry between unconditional assertions and unconditional questions: Multiple assertions can be merged while multiple questions cannot. In particular, the data provides evidence for the immediacy
requirement of question acts: Issues must be resolved first. Questions
are more dependent on the immediate context than assertions because a
question must be followed by an answer. More specifically, an unconditional question pragmatically presupposes specific answers, namely unconditional assertions. Without an appropriate con- text, it fails to satisfy the
Pragmatic Presupposition of Questions resulting in a presupposition failure or else it violates the following constraints regarding how the discourse
should proceed, No Vacuous Moves and Isaacs and Rawlins’ Inquisitive Constraint. I formally articulated the resistance against merger
of conditional questions and the immediacy requirement of questions by
providing an extension of Kaufmann’s stack-based model for conditionals and other related notions, which can deal with the multiple contexts
created by unconditionals.
1
1
Introduction
Operations over question acts seem to be more restricted than operations over
assertions. This paper presents a novel set of data which demonstrates that
issues raised by questions are more dependent on the immediate context than
the information brought by assertions. To see how this generalization is reached,
let us start with the following English conditional declarative in (1). In view of
the dynamic semantics of conditionals (Stalnaker, 1968; Karttunen, 1974; Heim,
1982), the antecedent serves to restrict the context of the consequent assertion.
Thus, in the case of the conditional declarative like (1), the antecedent clause
first temporarily updates the context with its propositional content. Second, the
consequent clause updates the derived context with its propositional content.
(1)
If the party is at Emma’s place, it will be fun.
A conditional interrogative like (2) can be analyzed in a parallel way as done
by Isaacs & Rawlins (2008). That is, just like the conditional declarative, the
antecedent clause creates a temporary context by updating the current context
with its content, and then the consequent interrogative inquisitively updates,
i.e., partitions the temporary context in the sense of Groenendijk (1999).
(2)
If the party is at Emma’s place, will it be fun?
Now, the parallel between declaratives and interrogatives breaks down when
the if -adjunct is replaced with adjuncts of so-called unconditionals (Rawlins,
2008, 2013). In a nutshell, an unconditional statement creates a set of conditional statements and ‘merges’ them, the result of which is semantically equivalent to the conjunction of the conditional statements (see Section 4 for formal
details).1 As a result, the construction expresses a conjunction of multiple conditional assertions, e.g., ‘If the party is at Emma’s place, it will be fun and if
the party is not at Emma’s place, it will be fun’. For instance, a declarative
modified by a whether-or-not -adjunct is grammatical and gives rise to the unconditional interpretation as in (3). That is, (3) means that the party will be
fun and it does not matter whether or not it is at Emma’s place.
(3)
Whether or not the party is at Emma’s place, it will be fun.
In contrast, when the consequent is a question, the conditional if -adjunct
cannot be rendered into the unconditional whether-or-not -adjunct, as in (4).
(4)
*Whether or not the party is at Emma’s place, will it be fun?
Assuming (4) has a parallel structure to its declarative counterpart (3), the
ungrammaticality of (4) suggests that, unlike the case of assertions, merging
multiple questions is not a licit act. This asymmetry between assertions and
1I
owe this phrasing to an anonymous reviewer.
2
questions (summarized in (5)) is the main puzzle of the paper.2
(5)
a.
b.
‘if p, q’ and ‘if ¬p, q’ can be merged as an unconditional assertion
‘whether or not p, q’
(Rawlins, 2008, 2013)
‘if p, q?’ and ‘if ¬p, q?’ cannot be merged as an unconditional
question ‘whether or not p, q?’
In this paper, I take these data to show that questions are more dependent on
the immediate context than assertions because a question must be followed by an
answer. More specifically, an unconditional question pragmatically presupposes
specific answers, namely unconditional assertions. Without an appropriate context, it fails to satisfy the Pragmatic Presupposition of Questions resulting in a
presupposition failure or else it violates the following constraints regarding how
the discourse should proceed:3
(6)
No Vacuous Moves
Vacuous discourse moves are prohibited.
(7)
Inquisitive Constraint (informal)
A question has to be resolved first before the discourse proceeds.(Isaacs & Rawlins,
2008)
This paper is structured as follows. Section 2 first characterizes the puzzle to
be solved in this paper. Section 2.1 briefly reviews Rawlins’ (2008, 2013) static
analysis of unconditionals. Section 2.2 presents structures for (un)conditional
assertions and questions. More specifically, I argue that (un)conditional adjuncts serve as context-shifters for the update of the consequent clause. Section 2.3 presents the main proposal, claiming that an unconditional question
either causes a presupposition failure or a violation of No Vacuous Moves
and the Inquisitive Constraint. In order to formally motivate this proposal, in Section 3, I review Isaacs and Rawlins’s (2008) analysis of conditional
questions, which combines Kaufmann’s (2000) stack-based model for conditionals and Groenendijk’s (1999) partition semantics for questions. Adopting a
dynamic semantics for conditionals, in Section 4, I propose that the English unconditional adjuncts create multiple temporary contexts and extend Kaufman’s
(2000) model of conditionals. Also, new operations that can deal with multiple contexts are introduced. The asymmetry between assertions and questions
is explained by the violations of No Vacuous Moves and the Inquisitive
Constraint. Since an unconditional question forces illegal operations which
output a defective context, it is ruled out as an irrational discourse act. Section
5 concludes the paper.
2 A similar incompatibility between an interrogative and a cancellation of alternative acts
is observed for the Japanese dake-wa ‘only-topic’ construction. See also Section 5.2.
3 Thanks to the reviewer for suggesting to spell out the constraints.
3
2
Characterizing the puzzle
This section characterizes the puzzle of the asymmetry between unconditional
assertions and questions in detail by looking at the syntax and semantics of
unconditionals. I basically adopt the analysis of unconditionals proposed by
Rawlins (2008, 2013). However, I will extend the analysis into a dynamic framework, since the main theme of the paper involves the evolution of contexts via
the progression of discourse.
2.1
Rawlins (2008, 2013) on unconditionals
Rawlins (2008, 2013) claims that the structural/semantic difference between
conditionals and unconditionals is that the latter involves a Hamblin-style (1958)
interrogative structure.4 In a nutshell, the unconditional adjunct in (8) generates a set of exhaustive propositions, i.e., possible answers, `a la Hamblin (1958).
That is, the set {p, ¬p} denoted by the adjunct exhausts the context set.5
(8)
Whether or not the party is at Emma’s place, it will be fun.
The set-denoting adjunct is combined with the main clause through Hamblin’s point-wise functional application, which generates a set of conditional
sentences. Then, a default universal quantifier quantifies over the set, and the
whole construction denotes a conjunction of conditional statements, e.g., ‘If the
party is at Emma’s place, it will be fun, and if the party is not at Emma’s
place, it will be fun’. Since the content of the main clause stays constant, the
choice among possible answers does not affect the value of the main clause.
Furthermore, since the set of alternatives is exhaustive, the union of all the
alternatives {p, ¬p} covers the entire context. This is how the relational indifference (Rawlins, 2013) meaning, i.e., ‘it doesn’t matter wh-’, comes about
from an unconditional. In other words, an unconditional construction signifies
independence between the antecedent and the consequent.
In summary, an unconditional construction whether or not p, q semantically
encodes a conjunction of alternative conditional sentences ‘if p, q’ and ‘if not p,
q’. As a result, the construction implies the independence between p and q and
entails q, though Rawlins (2013) explicitly claims that the independence and
consequent entailment themselves are not directly encoded in the construction
4 More precisely, in Rawlins (2013), the antecedent of a conditional also denotes a Hamblinstyle set, which only has one member, i.e., a singleton set.
5 In a whether-or-not adjunct like (8), it is clear that alternative propositions are exhaustive. According to Rawlins (2008, 2013), however, even if the unconditional adjunct takes the
form of an alternative question as in (i), the alternative propositions are exhaustive since the
Hamblin-style question operator introduces exhaustivity and mutual exclusivity presuppositions. Thus, the adjunct ‘whether the party is at Emma’s place or at Fred’s place’ presupposes
(or “conveys a backgrounded speaker commitment” (Rawlins, 2013, 138)) that the party is at
Emma’s place or at Fred’s place.
(i)
Whether the party is at Emma’s place or at Fred’s place, it will be fun.
4
but simply arise as a result of semantic composition.6
2.2
Left and right-adjoined (un)conditional adjuncts
Rawlins’ (2008, 2013) analysis of unconditionals is based on a static analysis
of conditionals and provides a uniform semantics for left- and right-adjoined
adjuncts. As also observed by Rawlins (2008, 2013), however, unconditional
adjuncts cannot be left-adjoined to questions as in (9).7,8
(9)
a. *Whether the party is at Alfonso or Joanna’s house, will it last a long
time?
b. *Whoever comes to the party, will it last a long time?
c. *No matter who comes to the party, will it last a long time?
(adapted from Rawlins, 2008, p. 141)
On the other hand, the right-adjoined counterparts are significantly better,
though they may not be perfect.
(10)
a. Will the party last a long time whoever comes to it?
b. Will the party last a long time no matter who comes to it?
c. ?Will the party last a long time whether it’s at Alfonso or Joanna’s
house?
(Rawlins, 2008, p. 142)
Rawlins (2008, 2013) did not provide a full discussion but entertained a
hypothesis that the ungrammaticality of (9) could be analyzed by means of
an intervention effect (Beck & Kim, 2006; Shimoyama, 2006). The intervention
effect describes a problematic syntactic configuration in which a focus particle
such as only or even appears between the question operator and disjunction.
(11)
a. ?*Did only Mary introduce Sue or Molly to Bill?
b. ?*Does even John like Mary or Sue?
(Beck & Kim, 2006, p. 172)
6 The same notion of independence is used to explain other phenomena surrounding conditionals. For instance, van Rooij (2007) and Lassiter (2012) claim that presuppositions in
conditionals can be strengthened when the antecedent and consequent of a conditional presupposition are independent. Also, Franke (2007, 2009) argues that the intuition of consequent
entailment in biscuit conditionals can be derived from the assumption of independence between the antecedent and consequent. This notion of independence originates from Lewis’s
(1988) orthogonality of subject matter (i.e., questions/issues):
(i)
For a context c (a set of possible worlds):
Two issues (i.e., equivalence relations on c) P1 and P2 are independent/orthogonal in
c iff ∀w, v ∈ c : ∃u ∈ c : hu, wi ∈ P1 ∧ hu, vi ∈ P2 .
(adapted from Lewis, 1988)
Similarly, Kaufmann (2013) derives the interpretation of counterfactuals from causal dependency.
7 Thanks to the reviewer for pointing out the parallel between unconditionals and whenever clauses, which were the constructions that I originally discussed in the earlier version of this
paper.
8 Rawlins’ (2008) original judgment was #.
5
Rawlins (2008, 2013) suggests that an unconditional adjunct acts as an intervener when it is left-adjoined to an interrogative.
The following data, however, show that syntactic explanations like an intervention effect cannot be maintained. In (12), the consequent interrogatives
perform request speech acts, and they are judged as grammatical.
(12)
a.
b.
c.
d.
Whether the sign says it’s OK or not, can you smoke outside please?
Whether or not the sign says it’s OK, can you smoke outside please?
Whatever the sign says, can you smoke outside please?
Whenever you leave the room, could you turn off the lights?
Thus, questions with left-adjoined unconditional adjuncts are ungrammatical because unconditionals are incompatible with the question acts, not because
they are incompatible with interrogative clauses or sets of propositions denoted
by the clauses.
In the remainder of this subsection, I discuss the structural contrast between
left-adjoined and right-adjoined (un)conditional clauses and propose that a leftadjoined adjunct takes scope over a speech act operator while a right-adjoined
one is adjoined to a VP. Correspondingly, a left-adjoined (un)conditional is a
(un)conditionalized speech act (Krifka, To appear; Stalnaker, 2005), while in
a right-adjoined (un)conditional, the entire (un)conditional sentence is in the
scope of the speech act operator. In particular, it is observed that unconditional
clauses cannot left-adjoin to interrogatives which perform question acts.
Let us first look at declaratives. As we see in (13), both if - and whether-ornot -clauses can be left-adjoined or right-adjoined to a declarative sentence.
(13)
a.
b.
c.
d.
If the party is at Emma’s place, it will be fun.
The party will be fun if it is at Emma’s place.
Whether or not the party is at Emma’s place, it will be fun.
The party will be fun whether or not it is at Emma’s place.
I adopt the claim by Cinque (1999); Krifka (2001); Speas & Tenny (2003);
Speas (2004); Tenny (2006) that there are syntactic representations for speech
acts such as assert, quest, etc., and propose that the left-adjoined if -clause
is base-generated at the Spec position of a Speech Act Phrase (SAP), while the
right-adjoined if -clause is attached to VP and so is inside the scope of the speech
act operator.9 For instance, the structures of (13a) and (13b) are depicted below
as in (14a) and (14b), respectively.
9 Iatridou (1991) and Bhatt & Pancheva (2006) also argue that left-adjoined (sentenceinitial) if -clauses involve CP/IP adjunction while right-adjoined (sentence-final) ones involve
VP-adjunction.
6
(14)
a.
SAP
SAP
CP
assert
If the party is at Emma’s place
TP
it will be fun
b.
SAP
TP
assert
T′
NP
The party
will
VP
VP
be fun
CP
if it’s at Emma’s place
Correspondingly, I claim that left-adjoined (un)conditional adjuncts are contextshifters for the subsequent updates while right-adjoined counterparts can have
a static semantics of implication or quantification over events (Kratzer, 1991).10
Put another way, left-adjoined adjuncts serve as Austinian (1950) topics. That
is, the if -clause denotes what an utterance is about. The similarity between
if -clauses and topics are also discussed in Haiman (1978, 1993); Collins (1998);
Bhatt & Pancheva (2006).
In dynamic approaches to conditionals (Stalnaker, 1968; Karttunen, 1974;
Heim, 1982), a conditional sentence like (13a) is not a single assertive update
of a conditional proposition on the main context, but a creation of a temporary
context followed by an assertive update on the temporary context.11 I argue that
left-adjoined whether-or-not -clauses also always induce this two-step dynamic
procedure. On my implementation, the left-adjoined whether-or-not -clause in
(13c) creates multiple temporary contexts onto which the assertive update of the
consequent will be performed. Furthermore, extending Rawlins’ (2008; 2013)
static analysis which conjoins the set of conditional statements, I claim that
in unconditional constructions, all the updates are simultaneously performed.
Thus, (13c) can be paraphrased as follows:
10 See also Hacquard (2006) who argues that different flavors of modality can be derived
from the difference in the syntactic structures.
11 The formal details will be spelled out in Section 3.2.
7
(15)
[If the party is at Emma’s place, assert(it will be fun) and if the party
is not at Emma’s place, assert(it will be fun)].
When the consequent clause is an interrogative, however, a left-adjoined
whether-or-not -clause results in ungrammaticality as in (16c), though the rightadjoined counterpart (16d) is grammatical.
(16)
a. If we go to the party, will Mary be there?
b. Will Mary be at the party if we go there?
c. *Whether or not the party is at Emma’s place, will it be fun?
d. Will the party be fun whether or not it’s at Emma’s place?
Given that left-adjoined whenever -clauses are context-shifters, the difference
in grammaticality judgments between (13c) and (16c) suggests that merging
multiple inquisitive updates on shifted contexts is somehow disallowed. In other
words, (17) is an illicit operation.
(17)
*[If the party is at Emma’s place, quest(it will be fun) and if the party
is not at Emma’s place, quest(it will be fun)]
Now, how about the syntax and semantics of the right-adjoined (un)conditional
constructions? In particular, why can the unconditional clause right-adjoin to an
interrogative? As depicted in (14b), I claim that right-adjoined (un)conditional
clauses are adjoined to VPs. Thus, both the antecedent and consequent are
inside the scope of the speech act operator.12 In the case of unconditionals, the
conjunction of multiple conditional statements also takes place before the con12 One can further argue that the right-adjoined conditionals have the static semantics of
implication or quantification over events rather than acting as dynamic two-step assertions. It
may seem unconventional that both static and dynamic semantics are endorsed for conditional
sentences. In addition to the contrasts in grammaticality found with unconditional questions,
however, there is support for a semantic contrast between the right-adjoined and left-adjoined
conditional adjuncts corresponding to a structural contrast. For instance, donkey pronouns
can refer back to their antecedents inside a left-adjoined if -clause, but not to the ones inside
a right-adjoined if -clause:
(i)
a.
b.
If a farmer owns a donkey, he pats it.
*He pats it if a farmer owns a donkey.
Note that donkey pronouns can be cataphoric if they are inside a left-adjoined if -clause as
in (iia). Thus, the ungrammaticality of (ib) and (iib) shows the structural difference between
left-adjoined and right-adjoined if -clauses.
(ii)
a.
b.
If it is overcooked, a hamburger doesn’t taste good.
*It doesn’t taste good if a hamburger is overcooked.
(Chierchia, 1995, p. 129)
(Elbourne, 2009, p. 3)
More specifically, Elbourne (2009) claims that right-adjoined if -clauses are attached below
the subject, i.e., to VP, thus (ib) and (iib) violate Principle C of the Binding Theory, “Referential expressions must be free” (Chomsky, 1981). The claim is further supported by (iii). In
(iii), if the if -clause is adjoined to the VP, a hamburger is not c-commanded by its pronoun,
and hence it is not bound. Since Principle C is not violated, (iii) is correctly predicted to be
grammatical by the hypothesis that the right-adjoined if -clause is a VP adjunction.
(iii)
John won’t eat it if a hamburger is overcooked.
8
(Elbourne, 2009, p. 3)
struction merges with the speech act operator. Thus, the informal paraphrases
of (13d) and (16d) would be as follows:
(18)
a.
b.
assert([The party will be fun if it’s at Emma’s house and The
party will be fun if it’s not at Emma’s house])
quest([The party will be fun if it’s at Emma’s house and The
party will be fun if it’s not at Emma’s house])
In sum, this section presented data which show that whether-or-not -clauses
cannot be left-adjoined to interrogative consequents. The pattern is schematically summarized in (19).
(19)
a. If p, assert(q)
b. assert(q if p)
c. If p, quest(q)
d. quest(q if p)
e. Whether or not p, assert(q)
f. assert(q whether or not p)
g. *Whether or not p, quest(q)
h. quest(q whether or not p)
Given that the left-adjoined adjunct is a context-shifter and unconditional
constructions conjoin multiple speech acts, the data can be regarded as an
indication that merging assertions is a licit operation while merging questions
is not.
2.3
Proposal: Questions are immediate issues
Given the discussion above, the next question is: Why is there such an asymmetry between assertions and questions? While alternative assertion acts can
be merged, alternative question acts cannot. My answer is that questions raise
issues that need to be immediately resolved before merger, while assertions resolve issues, whereby feeding merger.13 Indeed, as we will see below, posing
multiple conditional questions is possible if the multiple issues can be resolved
by an unconditional answer.
Intuitively, a question is different from an assertion in that a question raises
an issue which needs to be resolved while an assertion merely brings a piece
of information. Thus, an assertion is a complete act by itself, while a question
needs to be followed by an answer. In other words, a question pragmatically
presupposes that there is an answer to the question:
(20)
ϕ pragmatically presupposes ψ iff whenever the utterance of ϕ is con-
Elbourne (2009) takes these data to argue that Elbourne’s (2005) static situation-based semantics of donkey anaphora can be maintained. Providing the semantics for donkey sentences is beyond the scope of this paper, but the structural contrast between the right- and
left-adjoined if -clauses stands firm. Since two conditional sentences have different syntactic
structures, they are not required to have the same semantics.
13 I would like to thank the reviewer for suggesting to rephrase this claim.
9
versationally acceptable, the speaker of ϕ assumes ψ.
Stalnaker, 1974)
(21)
Pragmatic Presupposition of Questions:
The addressee has an answer to the question.
Groenendijk & Stokhof, 1989)
(modified from
(c.f.,
This Pragmatic Presupposition of Questions can be coupled with more general pragmatic constraints such as Searlean (1969) felicity conditions and Gricean
(1975) Cooperativity. If one asks a question, then she wants to know an answer
to the question and she assumes that there is an answer that the hearer can provide. Put another way, these pragmatic constraints dictate that the questioner
should pose an answerable question.
Although all the native speakers I consulted find (16c) ungrammatical or
infelicitous, to some speakers, it can be improved if the context is such that the
speaker explicates the independence between the two issues, whether or not the
party is at Emma’s place and whether or not it will be fun as in (22). In other
words, the speaker is seeking an unconditional answer:14
(22)
A: I don’t think whether the party will be fun or not depends on
whether it is at Emma’s place or not. ?Now, whether or not the
party is at Emma’s house, will it be fun?
B1: Yes, whether or not it is at her house, it will be fun.
B2: No, whether or not it is at her house, it won’t be fun.
B3:#If it is at her place, it will be fun. If it is not at her place, it won’t
be fun.
As can be seen, the admissible answers to an unconditional question are
unconditional sentences like (22)-B1 and (22)-B2. Put another way, an unconditional question presupposes that the answerer has an unconditional answer.
Those possible responses are essentially unconditional assertions. As mentioned
in Section 2.1, unconditional assertions have the independence connotation that
the truth value of ‘the party will be fun’ is independent of that of ‘the party
is at Emma’s place’. Thus, the unconditional question is presupposing the set
of unconditional answers, which in turn give rises to independence between the
two issues. In (22), the first sentence ensures that this pragmatic presupposition is satisfied; hence the unconditional question is not impossible, though
not perfect.15 Otherwise, an unconditional question is a heavily pragmaticallyloaded question. If it is asked without any clear indication that the speaker
is expecting an unconditional answer as in (16c), it dissatisfies the Pragmatic
Presupposition of Questions causing a presupposition failure or a violation of
the Manner Maxim, and hence is judged anomalous.
If responding to an unconditional question is impossible due to the presupposition failure, how about analyzing it as a merged version of conditional
questions? Recall that an unconditional assertion is a merged version of con14 I
am grateful to the editor for bringing this contrast to my attention.
formal procedure is explicated in Section 4.2.
15 The
10
ditional assertions. Thus, the next question amounts to: While conditional
assertions can be merged, conditional questions cannot. Why is there such an
asymmetry?
In answering this question, I propose that merging questions is prohibited
because it would result in violations of the the following constraints, No Vacuous Moves and Isaacs and Rawlins’ (2008) Inquisitive Constraint.
(23)
No Vacuous Moves
Vacuous discourse moves are prohibited.
(24)
Inquisitive Constraint (informal)
The issue raised by a question has to be resolved first before the discourse proceeds.
The rest of the paper is devoted to formally motivating these constraints.
In order to see how they interact with unconditional constructions, the next
section presents Isaacs and Rawlins’s (2008) analysis of conditional questions.
3
Questions and Contexts
Isaacs & Rawlins (2008) analyze conditional sentences with interrogative consequents (conditional questions) like (25) using a dynamic semantics for conditionals and a partition semantics of questions.
(25)
If we go to the party, will Mary be there?
In analyzing conditional questions, Isaacs & Rawlins (2008) argue that questions affect the current context whereas assertions can affect the entire stack of
contexts. Employing Kaufmann’s (2000) temporary contexts for conditionals
and stack-based account of modal subordination, Isaacs and Rawlins suggest
that information conveyed by assertions can percolate down the stack while
issues raised by questions cannot.
3.1
Partition Semantics for Questions
Following Hamblin (1958, 1973) and others (Karttunen, 1977; Kratzer & Shimoyama,
2002), Isaacs and Rawlins assume that the meaning of a question is the set of
possible answers to the question. In terms of partition semantics, possible answers correspond to blocks in a partition of the set of possible worlds.16 To
implement this approach to questions in a dynamic semantics, Isaacs and Rawlins adopt Groenendijk’s (1999) analysis of questions, which defines the context
set as an equivalence relation on worlds. That is, the context set is a set of pairs
of worlds specifying a relation that is symmetric, transitive, and reflexive:
16 By definition, the blocks in a partition of the set are mutually exclusive and collectively
exhaust the set being partitioned. This property of a question becomes crucial in Section 3.3.
11
(26)
Definition: context
A context c is an equivalence relation on the set of possible worlds W .
(Groenendijk, 1999)
In a standard model of assertion (Stalnaker, 1968), where the context set is a set
of worlds, an assertive update removes worlds which make the assertive content
false. In the current framework, the context set is a set of world-pairs; hence
an assertive update amounts to deleting all pairs which contain a member that
makes the assertive content false.
(27)
Assertive update (⊕) on contexts:
For some context (set) c and clause φ:
c ⊕ φ = {hw1 , w2 i ∈ c | JφKw1 ,c = JφKw2 ,c = 1}
(Isaacs and Rawlins’ (2008) reformulation of Groenendijk (1999))
In contrast, a question does not remove worlds but disconnects worlds and
thereby partitions the context into blocks. That is, a question φ? removes pairs
that contain worlds, each of which resolves the question in a different way, i.e.,
assigns a different truth value to φ. If both worlds in the pair give the same
answer to φ?, the pair is kept, i.e., the worlds are still connected.
(28)
3.2
Inquisitive update (⊘) on contexts: For some context (set) c and clause
φ:
c ⊘ φ = {hw1 , w2 i ∈ c | JφKw1 ,c = JφKw2 ,c }
(Isaacs and Rawlins’ (2008) reformulation of Groenendijk (1999))
Stack-based Model for Conditionals
Given the dynamic view of assertive and inquisitive updates, conditionals are
characterized using a two step update procedure (Stalnaker, 1968; Karttunen,
1974; Heim, 1982):
(29)
a.
b.
A derived context is created by updating the speech context with
the antecedent of the conditional.
The derived context is updated with the consequent.
In implementing these steps, Isaacs and Rawlins employ Kaufmann’s (2000)
model of temporary contexts. Let us illustrate how Isaacs and Rawlins’ theory
derives the meaning of (25), repeated here as (30).
(30)
If we go to the party, will Mary be there?
In Kaufmann’s (2000) system, utterances are treated as operations over
macro-contexts, where a macro-context is a stack of contexts in Kaufmann
(2000) and Isaacs & Rawlins (2008):
(31)
Definition: macro-context
a. hi is a macro-context.
12
b.
c.
d.
If c is a (Stalnakerian) context and s is a macro-context, then hc, si
is a macro-context.
Nothing else is a macro-context.
If s is a macro-context, then sn is the nth context (counting from
0 at the top) and |s| is its size (excluding its final empty element).
(Isaacs & Rawlins, 2008, (43), p. 291)
Suppose that the initial input macro-context s (= hc, hii) for some context c is
defined as in (32) and that the facts of the worlds are as follows: ‘we’ are not
at the party in w1 , w2 , and ‘we’ are at the party in w3 , w4 ; Mary is at the
party in w1 , w3 , and Mary is not at the party in w2 , w4 . At the initial stage,
the conversational agent is ignorant about the context. That is, the agent has
no pre-existing commitments about facts or issues. Reflecting this state of the
context, all the worlds are connected and thereby treated as equivalent. This
initial context is diagrammatically depicted in (33). The lines indicate the
equivalence relations between worlds, and reflexive relations (e.g., hw1 , w1 i) are
omitted for readability.
(32)
s = hc, hii = s0 : c =

hw1 , w1 i hw2 , w1 i



hw1 , w2 i hw2 , w2 i
s0 :
hw1 , w3 i hw2 , w3 i



hw1 , w4 i hw2 , w4 i
hw3 , w1 i
hw3 , w2 i
hw3 , w3 i
hw3 , w4 i
hw4 , w1 i
hw4 , w2 i
hw4 , w3 i
hw4 , w4 i







(33)
w1
w3
w2
w4
In interpreting the antecedent of the conditional in (30), a temporary context
is created by making a copy of the initial context c. More precisely, a temporary
context is pushed onto the stack:
(34)
Definition: push operator
For any macro-context s and context c:
push(s, c) =def hc, si
(Isaacs & Rawlins, 2008, (44), p. 292)
13
The temporary context is assertive-updated according to (27). In a nutshell,
the function of the if -clause is defined as the macro-context change potential
(MCCP) which creates a temporary context that is assertive-updated by the
propositional content of the clause, as in (35):17
(35)
Definition: MCCP of an if -clause
For any macro-context s and if -clause [if φ]:
s + if φ =def push(s, s0 ⊕ φ)
Admittance condition: ‘If φ’ is admissible in a macro-context s iff s0 ⊕
φ 6= ∅
(adapted from Isaacs & Rawlins, 2008, (54), p. 297)
That is, all pairs which contain a member that makes the assertion false,
i.e., w1 and w2 , are removed from the temporary context, as in (36) and (37).
(36)
s′ = s +
[if [we are at the party]]=
hw3 , w3 i hw4 , w3 i
s′0 :
hw3 , w4 i hw4 , w4 i
s′1
c
(37)
The temporary context created:
w1
w3
w2
w4
In interpreting the question in the consequent, the derived context is partitioned
into two blocks. I will call a context that induces a (non-trivial) partition
‘inquisitive’ (following Groenendijk, 1999); thus an inquisitive update renders
the top-most context into an inquisitive context.
(38)
Definition: Inquisitive update on macro-contexts
For any macro-context hc, s′ i where c is the top member, and s′ is a
stack, and clause φ:
hc, s′ i + [Question φ] =def hc ⊘ φ, s′ i
(Isaacs & Rawlins, 2008, (49), p. 294)
Remember that Mary is at the party in w3 , and Mary is not at the party
in w4 . Since w3 and w4 resolve the question in different ways, the two worlds
are disconnected. In other words, the pairs that connect the two worlds are
17 The admittance condition encodes the presupposition that the propositional content of
the antecedent is possible, which is often assumed since Stalnaker (1968).
14
removed as in (39), and the temporary context is partitioned into two cells (40).
The pairs which resolve the question as yes are in bold.
(39)
s′′ = s′ +[will
Mary be there?]=
hw3 , w3 i
′′
s0 :
hw4 , w4 i
s′′1
c
(40)
The temporary context partitioned:
w1
w3
w2
w4
According to Isaacs and Rawlins, a yes-answer is an assertive update removing all the pairs that make the assertion (answer) false in the temporary context
as in (41) and (42).
(41)
s′′′ = s′′ +yes=
s′′′
0 :
s′′′
1 :
(42)

hw1 , w1 i



hw1 , w2 i
hw1 , w3 i



hw1 , w4 i
hw3 , w3 i
hw4 , w4 i
hw3 , w1 i
hw3 , w3 i
hw3 , w3 i
hw3 , w4 i
hw2 , w1 i
hw2 , w2 i
hw2 , w3 i
hw2 , w4 i
The temporary context updated:
w1
w3
w2
w4
hw4 , w1 i
hw4 , w3 i
hw4 , w3 i
hw4 , w4 i







This assertive update by the answer affects not only the temporary context
but also other members in the stack. That is, the information brought by
an assertion percolates down the stack. In characterizing this percolation of
15
information, the current framework adopts the notion of percolation ⊢ (‘support’
in Isaacs & Rawlins (2008)):
(43)
Definition of Percolation ⊢
For contexts c, c′ and c′′ :
A global context ⊢ (c, c′ , c′′ ) is defined as:
⊢ (c, c′ , c′′ ) =def
{hw1 , w2 i ∈ c|[¬∃w ∈ W.hw1 , wi ∈ c′ ∨ hw, w2 i ∈ c′ ] ∨
hw1 , w2 i ∈ c′′ }
(adapted from Isaacs & Rawlins, 2008, (46), p. 293)
‘⊢ (c, c′ , c′ ⊕ φ)’ can be read as ‘Discourse participants learn in a context c
that another context c′ supports φ’. In other words, ‘⊢ (c, c′ , c′ ⊕ φ)’ amounts
to keeping the worlds that: 1. do not appear as a member of the pairs in c′ ; or
2. are in (c′ ⊕ φ) (= c′′ ).
With this notion of percolation ⊢, Isaacs and Rawlins’ assertive updates on
macro-contexts are also carried over to the current framework.
(44)
Assertive update on macro-contexts
For any macro-context s and clause φ
s + [Assert φ] =def s′ where |s′ | = |s| = n
and s′i = ⊢g (si , s0 , s0 ⊕ φ) for all i, 0 ≤ i < n
(adapted from Isaacs & Rawlins, 2008, (47), p. 293)
As illustrated in (45) and (46), the update removes pairs which contain
worlds where the antecedent is true and the consequent is false (w4 : ‘we’ are at
the party and Mary is not there.).
(45)
s′′′ = s′′ +yes=
s′′′
0 :
s′′′
1 :
(46)

hw1 , w1 i



hw1 , w2 i
 hw1 , w3 i


hw1 , w4 i
hw3 , w3 i
hw4 , w4 i
hw3 , w1 i
hw3 , w3 i
hw3 , w3 i
hw3 , w4 i
hw2 , w1 i
hw2 , w2 i
hw2 , w3 i
hw2 , w4 i
The main context updated:
w1
w3
w2
w4
16
hw4 , w1 i
hw4 , w3 i
hw4 , w3 i
hw4 , w4 i







After the question is resolved, so that the temporary context is no longer
inquisitive, the temporary context can be popped off the stack according to (47)
as illustrated in (48).18
(47)
Definition: pop operator
For any macro-context hc, s′ i:
pop(hc, s′ i) =def hc, s′ i if s′ = hi, s′ otherwise
(Isaacs & Rawlins, 2008, (45), p. 292 )
(48)
′′′
s′′′′ = pop(s
 )=
hw1 , w1 i



hw1 , w2 i
′′′′
s0 :
 hw1 , w3 i


hw2 , w1 i
hw2 , w2 i
hw2 , w3 i
hw3 , w1 i
hw3 , w3 i
hw3 , w3 i







In general, derived contexts are discarded after the interpretation of declarative conditionals. Subsequent utterances do not refer back to the temporary
contexts. In contrast, Isaacs and Rawlins propose that derived contexts are not
discarded after the interpretation of interrogative conditionals, since the derived
contexts are still inquisitive. This requirement is formulated as the Inquisitive
Constraint, stated informally in (7), rephrased formally here in (49).
(49)
Inquisitive Constraint (formal)
A macro-context may not be popped if the top element is inquisitive.
(Isaacs & Rawlins, 2008, (49), p. 294)
Accordingly, information introduced by assertions percolates down the stack
but issues raised by questions do not. If issues percolated down the stack,
it would yield a defective context. This point made by Isaacs and Rawlins
is particularly relevant to the current paper, since I argue that unconditional
questions encode irrational discourse moves. Thus, I will expand on this idea in
the next section.
3.3
Exclusivity and Exhaustivity in Questions
Why do issues, i.e., inquisitive contexts, not percolate down the stack? In other
words, why do questions not affect the other members of the stack? According to Isaacs and Rawlins, percolating issues would result either in abandoning
exhaustivity or in abandoning mutual exclusivity. Recall that issues are partitions of the context set. In mathematics, “a partition of a set S is a collection
of mutually disjoint, non-empty subsets of S whose union is S” (Joshi, 1989):
(50)
A set P is a partition of a set S iff:
a. ∅S6∈ P
b.
P =S
(exhaustivity)
18 The definition in (47) itself does not determine when the pop operation applies. The
Inquisitive Constraint (49) prohibits a pop operation from applying to a stack with an
inquisitive context.
17
c.
[X ∈ P & Y ∈ P & X 6= Y ] → X ∩ Y = ∅
(mutual exclusivity)
Since an issue or a set of possible answers is defined as a partition, an issue
is by definition required to be collectively exhaustive and mutually exclusive.19
Going back to the issue raised by a conditional question, a derived context
created by a conditional is a context where some of the worlds in the initial
context have been removed. Hence, if an issue percolated, we would have to do
something extra to the worlds which were not included in the derived context
in order to maintain exhaustivity and mutual exclusivity. Pairs in s1 which
contain worlds that are not partitioned in s1 are in blue in the table. Pairs
which resolve the question as yes are in bold.
hw3 , w3 i
s0 :
hw4 , w4 i


hw1 , w1 i hw2 , w1 i hw3 , w1 i
hw4 , w1 i 



(51)


hw1 , w2 i hw2 , w2 i hw3 , w2 i
hw4 , w2 i
s1 :
hw1 , w3 i hw2 , w3 i hw3 , w3 i






hw1 , w4 i hw2 , w4 i
hw4 , w4 i
If these extra world pairs are added to both blocks of the partition specified in
the derived context, then the resulting relation does not obey mutual exclusivity,
as illustrated in (52).20
(52)
Mutual exclusivity abandoned in the main context:
19 Recall that according to Rawlins (2008, 2013), an alternative question like (ia) also denotes
a Hamblin-set. That is, the question has a presupposition that the party is at Emma’s place
or at Fred’s place. Thus, the set denoted by the question exhausts the context set. Likewise,
the set denoted by the corresponding unconditional adjunct like (ib) also exhausts the context
set, hence partitions the context.
(i)
a.
b.
Is the party at Emma’s place or at Fred’s place?
Whether the party is at Emma’s place or at Fred’s place, it will be fun.
20 In recent work on inquisitive semantics by Groenendijk and his colleagues (Groenendijk,
2007; Sano, 2009; Ciardelli & Roelofsen, To appear), mutual exclusivity is not treated as a
principal property of questionhood. Isaacs and Rawlins also give an alternative inquisitive
update operation which allows issues to percolate immediately, in which mutual exclusivity is
not strictly enforced. Furthermore, according to Isaacs and Rawlins, the alternative version
gives a simpler analysis for embedded conditional questions. However, even if issues percolate
down the stack, the topmost context must be exclusive and exhaustive. Furthermore, the
Inquisitive Constraint (49) must be maintained.
18
w1
w3
w2
w4
On the other hand, if we put those worlds in no block, as in (53), we end up
abandoning exhaustivity.
(53)
Exhaustivity abandoned in the main context:
w1
w3
w2
w4
Since questions must obey exhaustivity and mutual exclusivity (Hamblin, 1958;
Groenendijk & Stokhof, 1997), issues cannot percolate. Questions can only partition the top-most context. Furthermore, assuming that percolation precedes
the pop operation, an inquisitive (i.e., partitioned) context can never be popped
without being resolved, as stated in the Inquisitive Constraint, repeated
here as (54):
(54)
Inquisitive Constraint (formal)
A macro-context may not be popped if the top element is inquisitive.
(Isaacs & Rawlins, 2008, (49), p. 294)
Isaacs and Rawlins also discuss modally subordinated questions. The issue
raised by B’s question in (55) is relevant only in the temporary context created
by A’s utterance. The questioner is not interested in whether A would be upset
when no thief broke in.
(55)
A: A thief might break in.
B: Would you be upset?
A question in a modally subordinated context partitions only the topmost
context of the stack. Within that context, each block of the alternatives in the
partition is mutually exhaustive and mutually exclusive. The modally subordinated issue does not have to deal with the cases where a thief did not break
19
in.
In short, Isaacs and Rawlins argue that only the topmost context in the
stack can be partitioned, and issues raised by questions must be resolved before
the context is popped. If issues were forced to percolate down the stack, the
resulting context would be defective, i.e., non-exhaustive or non-exclusive. As
we will see below, unconditional questions force issues to percolate, thus they
are illicit as irrational discourse moves.
4
Analysis: Going Back to the Puzzle
Now, let us return to the puzzle I raised in the beginning: When multiple contexts are created, alternative assertive updates can be merged, while alternative
inquisitive updates cannot. Why is there such an asymmetry? My answer is
that merging inquisitive contexts would result in the violation of No Vacuous
Moves which prohibits utterances with no effects. Furthermore, due to the
Inquisitive Constraint, hypothetical issues raised by conditional questions
must percolate down the stacks. As seen in Section 3.3, this percolation of issues
results in a defective context. In short, an unconditional question is anomalous
because processing it violates two constraints, No Vacuous Moves and the
Inquisitive Constraint. In order to derive the desired interpretation for unconditional assertions and the anomaly of unconditional questions, this section
provides an extension of the model and notions introduced in Kaufmann (2000)
and Isaacs & Rawlins (2008). In particular, I introduce the notion of multi-stack
and the operators n-copy, merge, and M(ulti-)S(tack)pop in order to handle the
multiple contexts.
4.1
Assertions on multiple contexts
As argued in Section 2.2, the left-adjoined whether-or-not -clause like (56) takes
scope over the assert operator, as depicted in (57), and gives rise to a dynamic
interpretation of conditionals.
(56)
Whether or not the party is at Emma’s place, it will be fun.
(57)
SAP
SAP
CP
assert
Whether or not the party is at Emma’s place
TP
it will be fun
As sketched in Section 3.2, in the dynamic framework adopted in this paper, an if -clause restricts the context for the speech act of the consequent.
20
Now, according to Rawlins’ (2008, 2013) static analysis of unconditionals summarized in Section 2.1, an unconditional statement is a collection of alternative
conditional statements. Taken together, I propose that whether-or-not -adjuncts
create multiple temporary contexts, and the speech act modified by the whetheror-not -clause operates over those multiple contexts.
In implementing this proposal, I introduce the notion of multi-stack, as in
(58). A multi-stack is a sequence of stacks.
(58)
Definition: multi-stack
S := hs(0) , s(1) , s(2) , ...s(n) i is a multi-stack, where s(i) is a macrocontext and |s(0) | = ... = |s(n) |.
The context can be rendered into a multi-stack by using the n-copy operator
(59) when necessary, i.e., when multiple speech act updates are performed on
multiple contexts.
(59)
Definition: n-copy operator
For any macro-context s:
n-copy(s) =def hs(0) , ..., s(n−1) i, where s = s(0) = ... = s(n−1)
This n-copy operation can be understood as playing the role of the f-feature
in Rooth (1985, 1992) or the [Q] operator in Rawlins (2008, 2013). Like them,
it generates a set of Hamblin alternatives, A. When the alternative set takes
scope over a speech act operator, a multi-stack S is created (|S| = |A|) and
each member of the alternative set creates a hypothetical context on top of each
stack in S.
To illustrate, take the context in (60). At world w1 , the party is at Emma’s
place and it will be fun. At w4 , the party is not at Emma’s place and it will
not be fun.
(60)
w1
w2
w3
w4
@Emma(party)
+
+
−
−
fun(party)
+
−
+
−
The initial context has the form of a single stack as in (61).
(61)
a.
b.
s = hc, hii = s0 : c =

hw1 , w1 i hw2 , w1 i



hw1 , w2 i hw2 , w2 i
s0 :
hw1 , w3 i hw2 , w3 i



hw1 , w4 i hw2 , w4 i
hw3 , w1 i
hw3 , w2 i
hw3 , w3 i
hw3 , w4 i
hw4 , w1 i
hw4 , w2 i
hw4 , w3 i
hw4 , w4 i
The initial ignorant and indifferent context
21







w1
w3
w2
w4
When the whether-or-not -adjunct is processed, the interpreter realizes that
two stacks will be created.21 In other words, a whether-or-not -adjunct denotes
a macro-context change potential which creates a multi-stack and performs an
update over the created multi-stack:
(62)
Definition: MCCP of an whether-or-not φ, ψ
For a macro-context s and an unconditional statement [[whether or not
φ] ψ]:
s + [[whether or not φ] ψ] =def
hs(0) +[if φ]+assert ψ, s(1) + [if ¬φ]+assert ψi,
where hs(0) , s(1) i =2-copy(s).
Thus, the main macro-context is first rendered into a sequence of macrocontexts:
(63)
2-copy(s)=

hw1 , w1 i


hw1 , w2 i

 hw1 , w3 i
hw1 , w4 i
hw2 , w1 i
hw2 , w2 i
hw2 , w3 i
hw2 , w4 i
s(0)
hw3 , w1 i
hw3 , w2 i
hw3 , w3 i
hw3 , w4 i
hw4 , w1 i
hw4 , w2 i
hw4 , w3 i
hw4 , w4 i






hw1 , w1 i


hw1 , w2 i

 hw1 , w3 i
hw1 , w4 i
hw2 , w1 i
hw2 , w2 i
hw2 , w3 i
hw2 , w4 i
s(1)
hw3 , w1 i
hw3 , w2 i
hw3 , w3 i
hw3 , w4 i
Second, (62) performs the MCCP of an if -clause (35) in each of the macrocontexts. The definitions of an if -clause (35), assertive update (27) and the push
operator (34) are directly carried over to the current framework and repeated
here as (64), (65) and (66), respectively.
(64)
Definition: MCCP of an if -clause
For any macro-context s and if -clause [if φ]:
s+ if φ =def push(s, s0 ⊕ φ)
21 More
(i)
a.
b.
than two stacks can be created with other kinds of unconditionals:
Whenever the party is at Emma’s place, it will be fun.
Whoever throws the party, it will be fun.
In any case, the set of propositions denoted by the adjunct is a Hamblin set, so the set exhausts
the context set.
22
hw4 , w1 i
hw4 , w2 i
hw4 , w3 i
hw4 , w4 i





Admittance condition: ‘If φ’ is admissible in a macro-context s iff s0 ⊕
φ 6= ∅
(65)
Assertive update (⊕) on contexts:
For some context (set) c and clause φ:
c ⊕ φ = {hw1 , w2 i ∈ c | JφKw1 ,c = JφKw2 ,c = 1}
(66)
Definition: push operator
For any macro-context s and global context c:
push(s, c) =def hc, si
In effect, one temporary context is created in each stack, the top member
′(1)
of s′(0) is assertively updated with p, and s1 is updated with ¬p:
′(0)
s1
(67)
a.
b.
s + [whether or not [the party is at Emma’s place]]=

hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′(0)
hw1 , w1 i
hw2 , w1 i
hw1 , w2 i
hw2 , w2 i
hw2 , w1 i
hw3 , w1 i
hw4 , w1 i
hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i
hw2 , w4 i
hw3 , w4 i
hw4 , w4 i
The temporary contexts created:
′(0)
s0 :






hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′(1)
hw3 , w3 i
hw4 , w3 i
hw3 , w4 i
hw4 , w4 i
hw2 , w1 i
hw3 , w1 i
hw4 , w1 i
hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i
hw2 , w4 i
hw3 , w4 i
hw4 , w4 i
′(1)
s0 :
w1
w3
w1
w3
w2
w4
w2
w4
′(0)
The consequent of (56), ‘it will be fun’, removes w2 from s1 and w4 from
′(1)
s1 . This information can percolate down to the original member of the stack
by the operation of the assertive update on macro-contexts (44), repeated here
as (69), defined on the basis of Percolation ⊢ (43), repeated here as (68).
(68)
Definition of Percolation ⊢
For contexts c, c′ and c′′ :
A global context ⊢ (c, c′ , c′′ ) is defined as:
⊢ (c, c′ , c′′ ) =def
{hw1 , w2 i ∈ c|[¬∃w ∈ W.hw1 , wi ∈ c′ ∨ hw, w2 i ∈ c′ ] ∨
hw1 , w2 i ∈ c′′ }
(69)
Assertive update on macro-contexts
For any macro-context s and clause φ
s + [Assert φ] =def s′ where |s′ | = |s| = n
23





and s′i = ⊢g (si , s0 , s0 ⊕ φ) for all i, 0 ≤ i < n
According to (69), the temporary contexts are updated with the information
of the consequent and the original members of the stacks are also updated, as
in (70).
(70)
a.
b.
hs′(0) + [assert [it will be fun]], s′(1) + [assert [it will be fun]]i =

hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′(0)
hw1 , w1 i
hw2 , w1 i
hw1 , w2 i
hw2 , w2 i

hw2 , w1 i
hw3 , w1 i
hw4 , w1 i 

hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i 

hw2 , w4 i
hw3 , w4 i
hw4 , w4 i
The temporary contexts updated:
′′(0)
s0 :
′′(1)
s0

hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′(1)
hw3 , w3 i
hw4 , w3 i
hw3 , w4 i
hw4 , w4 i

hw4 , w1 i 
hw2 , w1 i
hw3 , w1 i

hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i 

hw2 , w4 i
hw3 , w4 i
hw4 , w4 i
:
w1
w3
w1
w3
w2
w4
w2
w4
After the percolation, i.e., the assertive update on macro-contexts, the temporary contexts are popped from the entire multi-stack. I now define MSpop,
an operator which performs the pop operation (47), repeated here as (72), on
each member of the multi-stack.
(71)
Definition: MSpop (multi-stack pop)
For any multi-stack S:
MSpop(S) =def hpop(s(0) ), ..., pop(s(n) )i.
(72)
Definition: pop operator
For any macro-context hc, s′ i:
pop(hc, s′ i) =def hc, s′ i if s′ = hi, s′ otherwise
(73)
a.
MSpop(hs′′(0) , s′′(1) i) = hpop(s′′(0) ), pop(s′′(1) )i =

hw1 , w1 i



hw1 , w3 i



hw1 , w4 i
s′′′(0)
hw3 , w1 i
hw3 , w3 i
hw3 , w4 i

hw4 , w1 i 


hw4 , w3 i 


hw4 , w4 i
24

hw1 , w1 i



hw1 , w2 i
hw1 , w3 i



s′′′(1)
hw2 , w1 i
hw2 , w2 i
hw2 , w3 i
hw3 , w1 i
hw3 , w2 i
hw3 , w3 i







′′′(0)
s0
′′′(1)
:
s0
:
w1
w3
w1
w3
w2
w4
w2
w4
b.
Now, as discussed in Sections 2.1 and 2.3, in Rawlins’ (2008, 2013) static analysis, the unconditional or independence meaning of unconditionals comes from
universal quantification over the alternative conditional statements. In the current dynamic framework, the same effect is obtained from a merge operator
defined in (74) on the basis of (75).
(74)
Definition: merge operator
For a multi-stack hs(0) , s(1) i:
merge(s(0) , s(1) ) =def s(0) ∩ s(1)
(75)
Definition: stack intersection
For any stacks s, t, s ∩ t is defined if |s| = |t|.
If defined, s ∩ t =def u such that for all ui and 0 ≤ i ≤ |s|,
ui := si ∩ ti = {hw1 , w2 i|hw1 , w2 i ∈ si ∧ hw1 , w2 i ∈ ti }
The merge operator collapses the sequence of macro-contexts into a single
one as depicted in (76).
(76)
a.
b.
merge(s′′′(0) , s′′′(1) ) =
s′′′′

hw3 , w1 i
 hw1 , w1 i


hw1 , w3 i



hw3 , w3 i
s′′′′
0 :
25







w1
w3
w2
w4
As a result, we end up with the same information state as the case where the
initial context simply assertively updated with the consequent (77), as depicted
in (78).
(77)
The party will be fun.
(78)
a.
b.
s+[assert
 The party will be fun]=
 hw1 , w1 i hw2 , w1 i hw3 , w1 i


hw1 , w2 i hw2 , w2 i hw3 , w2 i
s′0 :
 hw1 , w3 i hw2 , w3 i hw3 , w3 i


hw1 , w4 i hw2 , w4 i hw3 , w4 i
s′0 :
w1
w3
w2
w4
hw4 , w1 i
hw4 , w2 i
hw4 , w3 i
hw4 , w4 i







This is as desired. The unconditional whether-or-not p, q entails p, hence
the consequent entailment.
In unconditional assertions, the percolation is a licit move. The fact that
the temporary context of each stack might contain different information does
not cause a further complication for the merge operation, since all an assertion
does is remove the same worlds, those that make the propositional content false,
from both the temporary and main contexts. As we will see below, questions
cannot be merged since this involves a more complicated operation.
26
4.2
Questions on multiple contexts
Now, let us turn to the cases with question consequents. As we have seen in
section 3, the conditional question (79) partitions the temporary context created
by the antecedent. If an answer is given, the information brought by the answer
percolates down the stack and the temporary context is popped.
(79)
If the party is at Emma’s place, will it be fun?
In cases of questions with a whether-or-not -clause like (80), the whether-or-not clause creates a sequence of stacks in the same fashion as depicted in (67a) for
the assertion case.
(80)
*Whether or not the party is at Emma’s place, will it be fun?
The question act of the consequent then operates over those contexts, i.e.,
partitions each context (28), as repeated in (81).
(81)
Inquisitive update (⊘) on contexts: For some context (set) c and clause
φ:
c ⊘ φ = {hw1 , w2 i ∈ c | JφKw1 ,c = JφKw2 ,c }
When operating on macro-contexts, the inquisitive update is crucially different
from the assertive update. The reason is that an inquisitive update as defined
by Isaacs and Rawlins only operates on the top element:
(82)
Inquisitive update on macro-contexts
For any macro-context hc, s′ i where c is the top member, and s′ is a
macro-context, and clause φ
hc, s′ i + [Question φ] =def hc ⊘ φ, s′ i
(Isaacs & Rawlins, 2008, (48), p. 294)
The following diagrams illustrate the creation of temporary contexts and
how they are partitioned:
(83)
a.
hs′(0) +[quest [it will be fun]], s′(1) +[quest [it will be fun]]i =
b.

hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′(0)
hw1 , w1 i
hw2 , w1 i
hw1 , w2 i
hw2 , w2 i
hw2 , w1 i
hw3 , w1 i
hw4 , w1 i
hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i
hw2 , w4 i
hw3 , w4 i
hw4 , w4 i
The temporary inquisitive contexts:
27






hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′(1)
hw3 , w3 i
hw4 , w3 i
hw3 , w4 i
hw4 , w4 i
hw2 , w1 i
hw3 , w1 i
hw4 , w1 i
hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i
hw2 , w4 i
hw3 , w4 i
hw4 , w4 i





s′′(0) :
s′′(1) :
w1
w3
w1
w3
w2
w4
w2
w4
This is the point at which assertions and questions diverge. An assertion
is a complete act by itself as it only removes worlds from the context set. In
contrast, a question needs to be followed by an answer, since a question renders
the context inquisitive, which needs to be resolved by information brought by
the answer. In other words, a question presupposes that there is an answer
to the question. As discussed in Section 2.3, to at least some speakers, it is
not impossible to resolve the multiple issues depicted in (83a) by giving an
unconditional answer if the context is appropriate.
(84)
A: I don’t think whether the party will be fun or not depends on
whether it is at Emma’s place or not. ?Now, whether the party is
at Emma’s place, will it be fun?
B: Yes, whether or not the party is at her place, it will be fun.
(84)-B is an unconditional assertion. Thus, it can resolve the issues in the
temporary contexts, percolate the information down the stacks, and pop the
temporary contexts by following the steps presented in Section 4.1.
(85)
hs′′(0) +[assert [it will be fun]], s′′(1) +[assert [it will be fun]]i =

hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′(0)
hw1 , w1 i
hw2 , w2 i
hw2 , w1 i
hw3 , w1 i
hw4 , w1 i
hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i
hw2 , w4 i
hw3 , w4 i
hw4 , w4 i






hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′(1)
hw3 , w3 i
hw4 , w4 i
hw2 , w1 i
hw3 , w1 i
hw4 , w1 i
hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i
hw2 , w4 i
hw3 , w4 i
hw4 , w4 i
However, if an unconditional question is posed out of context, it is most
likely to cause a presupposition failure by violating the Pragmatic Presupposition of Quesionts, which explains the anomaly of (80). Now, recall that an
unconditional assertion is analyzed as a conjunction of conditional assertions.
If the multiple hypothetical issues cannot be resolved, how about merging questions? Thus, the puzzle is: Why is (86a) not analyzed as a merged version of
(86b)?
(86)
a. *Whether or not the party is at Emma’s house, will it be fun?
b. If it is at Emma’s place, will it be fun? And if it is not at Emma’s
place, will it be fun?
28





In the following, I argue that merging conditional questions is an illicit operation
since it ends up violating either No Vacuous Moves or the Inquisitive Constraint. Informally speaking, assertions can be meaningfully merged, while
merging questions is prohibited since it would result in defective contexts. This
asymmetry is due to the complexity of the question operation, namely the partitioning of the context.
4.2.1
No Vacuous Moves
Let us try to apply the merge operator (74) to the the multi-stack hs′′(0) , s′′(1) i
in (83a) where each of the top-most members is partitioned. The application of
merge, i.e., merge(s′′(0) , s′′(1) ), would yield the following stack:
(87)
merge(s′′(0) , s′′(1) ) =
s′′′
∅

hw1 , w1 i


hw1 , w2 i

 hw1 , w3 i
hw1 , w4 i
hw2 , w1 i
hw2 , w2 i
hw2 , w3 i
hw2 , w4 i
hw3 , w1 i
hw3 , w2 i
hw3 , w3 i
hw3 , w4 i

hw4 , w1 i 

hw4 , w2 i
hw4 , w3 i 

hw4 , w4 i
Since each of the topmost members in (83a) is a block of a partition, the
intersection of them is an empty set. Thus, the merged topmost member s′′′
0 is
now an absurd context. s′′′
is
not
an
inquisitive
context
hence
it
can
be
popped:
0
(88)
pop(s′′′ ) =

hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′′′
hw2 , w1 i
hw3 , w1 i
hw2 , w2 i
hw3 , w2 i
hw2 , w3 i
hw3 , w3 i
hw2 , w4 i
hw3 , w4 i

hw4 , w1 i 

hw4 , w2 i
hw4 , w3 i 

hw4 , w4 i
However, this is identical to the initial context. Thus, the unconditional question (79) ends up performing no update. Given that every utterance must be
meaningful in that it changed the context, vacuous updates should be prohibited. In other words, an unconditional question violates the constraint (23),
repeated here as (89).
(89)
No Vacuous Moves
Vacuous discourse moves are prohibited.
In short, assertions on derived contexts can be meaningfully merged, while merging questions would come back to the initial context making the utterance vacuous.
4.2.2
The issue must be resolved first
Finally, if the multiple issues cannot be resolved due to the presupposition failure
and conditional questions cannot be merged due to the vacuous outcome, can we
percolate down the issues? In Section 3.3, we have already seen that percolating
issues is prohibited by the Inquisitive Constraint (54), repeated here as (90).
29
(90)
Inquisitive Constraint (formal)
A macro-context may not be popped if the top element is inquisitive.
(Isaacs & Rawlins, 2008, (49), p. 294)
In the following, we will see how violating the Inquisitive Constraint
would yield a defective context.
Isaacs and Rawlins provide an immediate percolation version of the inquisitive update as in (91), which creates stacks as in (92).
(91)
Inquisitive update on macro-contexts (immediate percolation version)
For any macro-context s, and clause φ
s + [Question φ] =def s′ where |s′ | = |s| = n
and s′i = ⊢ (si , s0 , s0 ⊘ φ) for all i, 0 ≤ i < n
(adapted from Isaacs & Rawlins, 2008, (50), p. 295)
If the unresolved issues were forced to percolate down the stack according to
(91), the resulting lower contexts would be defective, i.e., either non-exclusive
or non-exhaustive.22
(92)
hs′(0) +[quest [it will be fun] , s′(1) +[quest [it will be fun]]i =

hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′(0)
hw2 , w1 i
hw1 , w1 i
hw1 , w2 i
hw2 , w2 i
hw2 , w1 i
hw3 , w1 i
hw4 , w1 i
hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw2 , w3 i
hw3 , w3 i
hw4 , w3 i
hw2 , w4 i
hw3 , w4 i
hw4 , w4 i






hw1 , w1 i


hw1 , w2 i
 hw1 , w3 i

hw1 , w4 i
s′′(1)
hw4 , w3 i
hw3 , w3 i
hw3 , w4 i
hw4 , w4 i
hw2 , w1 i
hw3 , w1 i
hw4 , w1 i
hw2 , w2 i
hw3 , w2 i
hw4 , w2 i
hw3 , w3 i
hw4 , w3 i
hw2 , w3 i
hw2 , w4 i
hw3 , w4 i
hw4 , w4 i





Thus, if we violate the Inquisitive Constraint (90) by creating and percolating multiple issues down the stacks, the discourse results in defective contexts.
If we observe the Inquisitive Constraint and let the multiple inquisitive contexts remain on top of the stack, the discourse cannot proceed.
Furthermore, merging these post-percolation contexts would not help. Let
us ignore the Inquisitive Constraint for a moment and perform MSpop on
the multi-stack S ′′ :
(93)
a.
MSpop(hs′′(0) , s′′(1) i) = hpop(s′′(0) ), pop(s′′(1) )i =

hw1 , w1 i



hw1 , w3 i



hw1 , w4 i
22 See
s′′′(0)
hw3 , w1 i
hw2 , w2 i hw3 , w2 i
hw2 , w3 i hw3 , w3 i
hw2 , w4 i hw3 , w4 i
(52) and (53) in Section 3.3 for the diagrams.
30
hw4 , w1 i
hw4 , w2 i
hw4 , w3 i
hw4 , w4 i








hw1 , w1 i



hw1 , w2 i
 hw1 , w3 i


hw1 , w4 i
s′′′(1)
hw2 , w1 i hw3 , w1 i
hw2 , w2 i hw3 , w2 i
hw2 , w3 i hw3 , w3 i
hw2 , w4 i

hw4 , w1 i 


hw4 , w2 i



hw4 , w4 i
s′′′(0) :
s′′′(1) :
w1
w3
w1
w3
w2
w4
w2
w4
b.
The result of the merge operation gives us a context which is still non-exhaustive
or non-exclusive, as depicted in (94b).
(94)
a.
merge(s′′′(0) , s′′′(1) ) =

hw1 , w1 i



b.
hw1 , w3 i



hw1 , w4 i
s′′′′ :
s′′′′
hw3 , w1 i
hw2 , w2 i hw3 , w2 i
hw2 , w3 i hw3 , w3 i
hw2 , w4 i

hw4 , w1 i 


hw4 , w2 i



hw4 , w4 i
w1
w3
w2
w4
Moreover, unlike unconditional assertions, the resulting context is not identical to the context which is inquisitively updated by an unmodified question
like (95).
(95)
Will the party be fun?
As in (96b), the updated context here is exhaustive and mutually exclusive:
(96)
a.
b.
s+[quest
 The party will be fun]=
hw1 , w1 i hw2 , w1 i hw3 , w1 i



hw
hw2 , w2 i hw3 , w2 i
1 , w2 i
s′0 :
hw
hw3 , w3 i
hw
,
w
i

2 , w3 i
1
3


hw1 , w4 i hw2 , w4 i hw3 , w4 i
s′0 :
31
hw4 , w1 i
hw4 , w2 i
hw4 , w3 i
hw4 , w4 i







w1
w3
w2
w4
Recall that in an unconditional assertion, the information percolates down
the stack and the multi-stack can be merged. As a consequence, it yields the
same context as a plain assertion without the whether-or-not adjunct. As can be
seen from comparing (94b) and (96b), unlike the unconditional assertion, the
unconditional question yields a defective (i.e., non-exhaustive/non-exclusive)
inquisitive context which is different from the partitioned context created by
the unmodified question. Thus, percolation of issues is an illicit move in the
discourse procedure.
In summary, unconditional questions are anomalous because they disobeys
the Pragmatic Presupposition of Questions resulting in a presupposition failure
or else the interpretation of them involves illicit operations that violate No
Vacuous Moves and the Inquisitive Constraint. Merging hypothetical
inquisitive contexts is prohibited because it would make the discourse move
vacuous. Forcing the percolation of the issues would yield a defective context.
5
5.1
Concluding Remarks
Summary
We have observed that questions are pragmatically more constrained than assertions. In particular, the data provided evidence for the immediacy requirement
of question acts: Issues must be resolved first. An assertion is a complete act by
itself while a question must be followed by an answer. In other words, a question
presupposes an answer. Due to this Pragmatic Presupposition of Questions, an
unconditional question presupposes an unconditional answer which entails the
independence between the unconditional “antecedent” and “consequent”. As a
result, an unconditional question is pragmatically heavy and likely to cause a
presupposition failure.
The data also shows that conditional questions cannot be merged, while an
unconditional assertion is a merged version of conditional assertions. I formally
articulated the resistance against merger of conditional questions and the immediacy requirement of questions by providing an extension of Kaufmann’s (2000)
stack-based model for conditionals and other related notions such as multi32
stacks, n-copy, merge, and MSpop operations, which can deal with the multiple
contexts created by unconditionals. More specifically, the presented data and
my analysis motivate two constraints on how a discourse should proceed, No
Vacuous Moves and Isaacs and Rawlins’ (2008) Inquisitive Constraint.
First, merging conditional questions results in a context identical to the initial
context. Thus, this operation violates No Vacuous Moves which requires any
utterance to have some effect, i.e., a change in the context set. Second, the
analysis reinforces the Inquisitive Constraint which dictates that the issue
has to be resolved before the temporary context is popped off. Percolating issues raised by conditional questions would yield a defective context. In short,
processing an unconditional question causes a presupposition failure; or else involves irrational discourse moves which would violate No Vacuous Moves or
the Inquisitive Constraint. As a result, left-adjoined unconditional adjuncts
are anomalous with question acts.
5.2
Future directions
There are several future directions for research related to this analysis. First, it
would be fruitful to investigate the Inquisitive Constraint cross-linguistically.
In particular, the current paper treats English left-adjoined if -clauses as Austinian topics. When a language has overt topic-marking, do we observe a similar
interaction with question acts? The answer is yes. Just like English if -sentences,
the Japanese topic-marking wa serves to shift the context. For instance, the assertion of the non-wa-marked (97a) could be about a general situation in an
airport, so the sentence is pragmatically implausible because it expresses a requirement that everyone at the airport has to be a dog-carrier. In contrast, the
phrase inu-wa in (97b) restricts the context of the assertion to cases where there
is a dog, so the sentence can reasonably be used in (for example) a sign in the
airport.
(97)
a.
b.
Inu-o
kakae nakerebanaranai.
dog-acc carry must
‘You must carry a dog.’
Inu-wa kakae nakerebanaranai.
dog-top carry must
‘As for dogs, you must carry them.’≈‘If there is a dog, you must
carry it.’
Wa-marked declaratives can be rendered into interrogatives without any
problem as in (98).23
(98)
a.
b.
23 Honorific
Inu-wa kakae nakerebanarimasen-ka?
dog-top carry must.hon-q
‘If there is a dog, do I have to carry it?’
John-wa ki-masi-ta-ka?
John-top come-hon-past-q
forms are added in order to make the examples pragmatically more natural.
33
‘As for John, did he come?’
But a familiar asymmetry obtains when another particle dake ‘only’ is added
to the wa-marked noun phrase. Following Rooth (1995), dake can be analyzed
as a focus particle which generates a Hamblin set of alternative propositions
and denies the truth of the alternatives except for the asserted one:
(99)
John-dake-ga kita.
John-only-top came
‘Only John came.’ (Others didn’t come. ≈ {Mary didn’t come, Bill
didn’t come,... })
When dake is used with wa, what is being denied is not alternative propositions but alternative assertion acts. That is, multiple contexts varying the
value of the sentence topic are created, and by using dake, the speaker makes it
explicit that among the alternative acts, the one with the prejacent topic is the
only assertion that the speaker is willing to make. Thus, the whole construction
seems to express exhaustification over possible assertion acts, as illustrated in
(100).
(100)
John-dake-wa ki-masi-ta.
John-only-top come-hon-past
‘Only as for John, he came.’ (I don’t make assertions about other
individuals; only>assertion)
As can be seen, an assertion with dake-wa involves the creation of multiple
contexts and denial of the rest of the alternative acts. (101) shows that this
complicated operation over speech acts is not available for questions:
(101)
*John-dake-wa nani-o
kai-masi-ta-ka?
John-only-top what-acc buy-hon-past-q
Although there is a difference between merging and denial of the alternative
acts, the parallel between English unconditional adjuncts and Japanese dake-wa
constructions suggests that the Inquisitive Constraint is one of the universal
principles of questionhood.
The treatment of commands is also an important outstanding issue within
this approach to the dynamics of speech acts and clause types. A command
can co-occur with unconditional adjuncts (102) and the dake-wa construction
(103b).
(102)
a.
b.
c.
Whether the sign says it’s OK or not, smoke outside!
Whenever you leave, remember to call me.
Whenever you have the time, come over and help us.
(103)
a.
Eigo-dake-o
benkyo-siro!
English-only-acc study-do.imp
‘Study only English!’ (Don’t study other subjects; command>only)
34
b.
Eigo-dake-wa
benkyo-siro!
English-only-con study-do.imp
‘Study at least English!’ (I don’t make orders about other subjects; only>command)
Also, note that if the question is not an information-seeking one, it is possible to have an interrogative with an unconditional adjunct as we have seen
above, repeated here as (104), and a question with wide-scope exhaustification
as in (105). Here, the question is interpreted as a request for action (like an
imperative) rather than a request for information.
(104)
a.
(105)
Denki-dake-wa keshi teoite-kure-masu-ka?
light-only-top off leave-ben-hon-q
‘Could you make sure that at least lights are off?’
(I don’t make other requests; only>request)
b.
Whether the sign says it’s OK or not, can you smoke outside,
please?
Whenever you leave, can I ask you to turn off the lights?
This data suggests that commands and requests should be treated as analogous to assertions. Future research on this topic will shed new light on the
taxonomy of speech acts.
References
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