Inquisitive pragmatics

1 Introduction
Inquisitive pragmatics ∗
(work in progress)
Matthijs Westera
February 21, 2013
Grice (1975) provided a framework for describing how we, as speakers, build
what we mean - speaker meaning - on top of what we literally say - sentence
meaning. Most existing accounts in Grice’s framework rely on a classical semantics
to provide the sentence meaning, but in principle any semantics might
do. Not surprisingly, which phenomena the Gricean framework can tackle depends
on the underlying semantics. These notes present a Gricean pragmatics
built upon unrestricted inquisitive semantics as formulated in (Ciardelli, 2009),
with the notion of entailment from (Westera, 2012). It enables an account of
exhaustivity implicatures, akin in spirit to (Westera, 2012), and it enables us to
model the implicatures of (some kinds of) partial answers and counter questions
and of the effect of rise-fall-rise intonation.
2 Inquisitive semantics
Following, e.g., (Groenendijk & Roelofsen, 2009), we conceive of propositions as
embodying proposals to update the common ground with one of several pieces
of information, the possibilities of the proposition. Let W be a set of possible
worlds, assigning truth values to the atomic formulae of a language of choice.
Definition 1 (Proposition, possibility)
A possibility a is a set of worlds, a ⊆ ℘W.
A proposition A is a set of possibilities, A ⊆ ℘℘W, with ∅ ∈ A.
That is, a proposition is a set of possibilities including at least the empty possibility
∅. This reflects the fact that, as Ciardelli (2009) remarks, the empty set
does not really make a contribution to how we conceive of a proposition as a
∗ Many thanks to Jeroen Groenendijk, Floris Roelofsen, Ivano Ciardelli, Elizabeth Coppock
and Thomas Brochhagen for helpful comments on various versions of this work. Financial
support from the Netherlands Organisation for Scientific Research (NWO) is gratefully
acknowledged.
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proposal, except perhaps when it is on its own. By, unlike Ciardelli, including
the empty possibility everywhere, we make sure it is of no importance when
it pops up in the construction of a proposition. Effectively, it functions as the
wastebasket of a proposition, and this will streamline some of the definitions to
come. 1
Propositions are assigned to formulae of propositional logic, given in Backus-
Naur Form:
Definition 2 (Syntax)
For p a propositional letter, formulae ϕ: ϕ ∶∶ ∣ p ∣ (ϕ ∧ ϕ) ∣ (ϕ ∨ ϕ) ∣ (ϕ → ϕ)
I will treat negation as a syntactic abbreviation according to ¬ϕ ∶= (ϕ → ).
For all formulae ϕ, let [ϕ] denote the proposition of ϕ. We define the semantics
recursively, following Ciardelli (2009), differing only in the empty possibility for
atomic formulae:
Definition 3 (Unrestricted inquisitive Semantics)
For p a proposition letter, ϕ, ψ formulae:
1. [p] = {{w ∈ W∣w(p) = true}, ∅}
2. [] = {∅}
3. [ϕ ∨ ψ] = [ϕ] ∪ [ψ]
4. [ϕ ∧ ψ] = [ϕ] ⊓ [ψ] (where A ⊓ B = {a ∩ b ∶ a ∈ A, b ∈ B})
5. [ϕ → ψ] = {{w∣ for all a ∈ [ϕ], if w ∈ a, then w ∈ f(a)}∣f ∶ [ϕ] → [ψ]}
We can conveniently use formulae also to talk about possibilities, i.e., the sets
of worlds contained in propositions:
Definition 4 (Possibility)
For all formulae ϕ, its possibility is given by ∣ϕ∣ = ⋃[ϕ].
The possibility of a formula is simply its classical set-of-worlds denotation.
2.1 Entailment
Following the algebraic characterisation of Westera (2012), entailment and containment,
as relations between propositions, are defined as follows: 2
Definition 5 (Entailment and containment) For all propositions A, B:
1. B entails A, B ⊧ A, iff ∃C, A ⊓ C = B
1 I have yet to explore the algebraic repercussions of this decision, left untouched in
(Westera, 2012). For one, it ensures that {∅} entails all propositions, just like contradictions
in classical logic would. I think this is desirable. Also, it avoids the difficult question of
what proposal the empty set would embody, because here, the empty set is not a proposition
to begin with.
2 Westera (2012) has a special name for the containment relation, namely ‘compliance’.
However, I now doubt both the usefulness of giving it a special name, and the appropriateness
of this name in particular.
2

2. B contains A, A ⊆ B, iff ∃C, A ∪ C = B
Note that in a classical semantics, and also in restricted (or ‘basic’) inquisitive
semantics, entailment and containment, defined in this way, would coincide.
Here, however, they are to some extent orthogonal, because the absorption laws
do not hold:
Fact 1 (No absorption laws)
Not generally for all propositions A, B: A ⊓ (A ∪ B) = A or A ∪ (A ⊓ B) = A.
This is easily verified for [p] ≠ [p ∨ (p ∧ q)], depicted in figure 1(b) and (c),
respectively.
The notion of entailment is rather sparse. For instance, it is easy to see that
we can never get from [p∨q] to [p], depicted in figure 1(a) and (b), via pointwise
intersection, without getting the additional possibility ∣p∧q∣, which is not in [p].
Hence, a disjunction is not generally entailed by one of its disjuncts. On the
other hand, [p∨q] is entailed by [p∨(p∧q)], depicted in figure 1(c). This shows
pq
✁pq
p ✁ q ✁ p ✁ q
(a) p ∨ q
pq
✁pq
p ✁ q ✁ p ✁ q
(b) p
pq
✁pq
p ✁ q ✁ p ✁ q
(c) p ∨ (p ∧ q)
Figure 1: Circles represent possible worlds. Shaded areas represent possibilities.
that entailment is sensitive to the internal structure of a proposition. 3 How
precisely it is sensitive can be seen by unpacking the definition of entailment:
Fact 2 (Entailment (unpacked)) For all propositions A, B:
B ⊧ A iff ∀b ∈ B, ∃a ∈ A, ∃c s.t. b = a ∩ c and ∀a ′ ∈ A, a ′ ∩ c ∈ B.
Here is an intuitive paraphrase: we look at all b ∈ B, which are the possibilities
we wish to construct from the conclusion, A. For any such b, we try to construct
3 Notably, entailment B ⊧ A does necessarily hold if every possibility of B is included in
one of A (pointwise inclusion), nor if both this and the reverse hold, that every possibility of
A contains one of B. The reader may verify this by comparing the following pair:
1. [(p ∧ q ∧ r) ∨ (p ∧ q ∧ ¬r)] ⊧ [p ∧ q]
2. [p ∨ (p ∧ q ∧ r) ∨ (p ∧ q ∧ ¬r)] /⊧ [p ∨ (p ∧ q)]
The only difference between the two, is that in the latter case, the propositions both contain
the overarching possibility ∣p∣.
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it by intersecting some a ∈ A, with some c, which can be any set of worlds. But
whichever c we choose, we have to intersect every other possibility a ′ ∈ A with
it as well, and this must not give any undesirable side-effects, i.e., possibilities
a ′ ∩ c that are not in B.
For some further insight, here is a characterisation of non-entailment, obtained
simply by flipping all the quantifiers to their duals, and negating the
inner conjunction, now read as an implication:
Fact 3 (Non-entailment) For all propositions A, B:
B /⊧ A iff ∃b ∈ B, ∀a ∈ A, ∀c, ∃a ′ ∈ A s.t. if b = a ∩ c; then a ′ ∩ c ∉ B.
This can be read as follows: for B to not entail A, it is sufficient if there exists
one b ∈ B that we cannot construct in any way without yielding an undesirable
side-effect, i.e., a possibility that is not in B. We try all combinations of any
a ∈ A with any possible c, but always there is some a ′ ∈ A that spoils it, because
a ′ ∩ c is a possibility not in B.
2.2 Fixing non-entailment by restricting the premiss
The following technical results will be directly relevant for inquisitive pragmatics.
Suppose for some A, B such that B /⊧ A, we were allowed to restrict the
premiss B to some set of worlds s in order to make the entailment go through.
The trivial fact that we will succeed can be stated as follows:
Fact 4 (Every non-entailment can be fixed)
For all propositions A, B, there is an s ⊆ W such that B ⊓ {s} ⊧ A
Of course this is true, since B ∩ {∅} entails everything. More usefully, the set
of all restrictions s that fix an entailment can be characterised by spelling out
the definition of entailment for the case with a restricted premiss:
Fact 5 (Which restrictions fix a non-entailment)
For all propositions A, B and s ⊆ W, B ⊓ {s} ⊧ A iff ∀b ∈ B, ∃a ∈ A, ∃c s.t.
1. b ∩ s = a ∩ c; and
2. ∀a ′ ∈ A, ∃b ′ ∈ B s.t. b ′ ∩ s = a ′ ∩ c.
This fact is not extremely transparent. 4 It is useful to explore how a nonentailment
can be fixed for some particular subclasses of propositions. First,
when the premiss contains only one possibility (besides the empty set), the
constraints on the restriction are as follows:
4 Despite the simple algebraic foundation of entailment, and its simple definition at the level
of propositions, it seems that at the level of possibilities there is no easy way to think about
entailment. In general, it is not difficult to see whether an entailment holds, by checking,
at the level of propositions, whether you can construct the premiss from the conclusion by
pointwise intersection; likewise it is generally quite easy to spot how the premiss may be
restricted to fix an entailment. It is just that, at the level of possibilities, the non-locality of
entailment makes the definitions cumbersome.
4

Fact 6 (Fixing entailment if B = {b, ∅})
For all propositions A, B, where B = {b, ∅}: B ⊓ {s} ⊧ A iff
1. ∃a ∈ A s.t. b ∩ s ⊆ a; and
2. ∀a ′ ∈ A, b ∩ s ⊆ a ′ or b ∩ s ⊆ a ′
Proof: Suppose the right-hand side is false, i.e., item 1. or 2. is false. If
1. is false, there is no a ∈ A s.t. b∩s ⊆ a, hence b∩s cannot be created and
therefore B⊓{s} /⊧ A. If 2. is false, then ∃a ′ ∈ A s.t. b∩s /⊆ a ′ and b∩s /⊆ a ′ ,
which means a ′ and b properly overlap, hence a ′ will create a side-effect
regardless of how b ∩ s is manufactored, and therefore B ⊓ {s} /⊧ A.
Suppose the right-hand side is true. Then according to item 1., ∃a ∈ A s.t.
b∩s ⊆ a, hence b∩s can be manufactured from a with some c, for instance
with c = b ∩ s. Furthermore, according to item 2., ∀a ′ ∈ A, b ∩ s ⊆ a ′ or
b ∩ s ⊆ a ′ , that is, all a ′ ∈ A must either contain or be disjoint with b ∩ s.
This ensures that if we manufacture b ∩ s by a ∩ b ∩ s, there will be no
side-effects, since for all a ′ , either a ′ ∩ b ∩ s = b ∩ s or a ′ ∩ b ∩ s = ∅.
Effectively, it is required of s that it implements either the material implication
from b to some a, or to its complement.
This result can be extended to propositions B of which all possibilities (except
the empty set) are disjoint, because in such cases all possibilities can be
created independently of one another, as if they were in separate propositions:
Fact 7 (Fixing entailment if all nonempty b ∈ B are disjoint)
For all propositions A, B s.t. ∀b, b ′ ∈ B, if b ≠ b ′ then b ∩ b ′ = ∅:
B ⊓ {s} ⊧ A iff ∀b ∈ B:
1. ∃a ∈ A s.t. b ∩ s ⊆ a; and
2. ∀a ′ ∈ A, b ∩ s ⊆ a ′ or b ∩ s ⊆ a ′
This is just fact 6, with the two requirements imposed on all b ∈ B. Fact 6 and 7
are all we need for the examples I will treat in the section below on pragmatics. 5
3 Inquisitive pragmatics
3.1 The conversational maxims
Grice (1975) argued that dialogue participants adhere to (and assume eachother
to adhere to) the cooperative principle:
Definition 6 (The cooperative principle (Grice, 1975)) Make your contribution
such as it is required, at the stage at which it occurs, by the accepted
purpose or direction of the talk exchange in which you are engaged.
5 Clearly, though, they will not suffice for future applications. In a future version I hope to
give similar accounts of the required restrictions when B ⊆ A or B ⊑ A (pointwise subset, i.e.,
∀b ∈ B, ∃a ∈ A s.t. b ⊆ a).
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From the cooperative principle a number of maxims can be derived that more
directly guide a speaker’s behaviour and a hearer’s interpretation of that behaviour.
These maxims fall in a number of categories, depending on whether
they pertain to the quantity of what is said (e.g., too much/too little information),
the relatedness of it to previous discourse (for Grice its ‘relevance’, but I
will avoid that term), the quality of what is said (e.g., its truth/falsehood), or
the manner in which it is said (e.g., whether it is clear and concise). Some of
an open-ended set of maxims are given below.
Definition 7 (Maxims) Propose a proposition only if:
1. you know it to be true; (Quality)
2. you consider its possibilities to be possible; (Quality)
3. relative to your knowledge state it entails the QUD; (Relation)
4. it supports as many of the QUD’s possibilities as possible; (Quantity)
5. its possibilities are not smaller than necessary for the above. (Quantity/Manner)
In these notes I will be concerned only with the first four maxims. Each of
these can be translated into a set of more formal constraints on the speaker’s
epistemic state:
Fact 8 (Epistemic constraints imposed by the maxims)
In response to a QUD A, the following holds for a cooperative speaker, with
knowledge state s, who utters B:
1. s ⊆ ⋃ B (Quality)
2. For all b ∈ B, a ∩ s ≠ ∅ (Quality)
3. B ⊓ {s} ⊧ A (Relation)
4. For all a ∈ A, if ⋃ B /⊆ a, then s /⊆ a (Quantity)
The constraints imposed by the qualitative maxims are quite straightforward.
For the third maxim, relation, facts 5, 6 and 7 can be used to spell out the
constraint in more detail. The fourth maxim embodies the requirement that
if the speaker can support a possibility, she must do so, and hence that if she
doesn’t, she must not be able to. This is typically how so-called ignorance
implicatures have always been derived in the literature since Grice, though with
variations on where the ‘what should have been said’ comes from.
Under the assumption that the speaker is cooperative, the epistemic constraints
in (8) translate directly into implicatures. These implicatures are due
to abiding the maxims, not, e.g., flouting them, which would yield a wholly
different class of implicatures that is outside our present scope.
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3.2 Exhaustivity implicatures
Among the implicatures we can account for is the exhaustivity implicature of
a reply to a disjunction. For brevity, I will formulate the implicatures below
in standard modal logic, with the familiar ◻ and ◇ indicating the epistemic
necessity and possibility for the speaker. That is, for a speaker with knowledge
state s, ◻ϕ iff s ⊆ ∣ϕ∣ and ◇ϕ iff s∩∣ϕ∣ ≠ ∅. The precise model-theoretic semantics
and axioms assumed for this modality are not important for our purposes (yet).
(1) a. Will John come, or Mary? (p ∨ q ∨ ¬(p ∨ q))
b. John will come.
Implicatures:
1. ◻(John will come) (Quality)
2. ◻(If John will come, then Mary will come) or
◻(If John will come, then Mary won’t come) or
◻(If John will come, then neither will come) (Relation)
3. ◇(Mary will not come) (Quantity)
4. ◻(Mary will not come) (from 1, 2 and 3)
Here the quantity implicature in 3 in effect disambiguates the relation implicature
in 2, together with 1. entailing that Mary won’t come, i.e., exhaustivity.
Notice that the third disjunct of the relation implicature in 2 is inconsistent
with the quality implicature in 1. In the next examples, I will therefore omit
such disjuncts from from the start.
In the same vein, we can account for the exhaustivity implicature in response
to a ternary disjunction:
(2) a. Will John come, or Mary, or Bob?
b. John will come.
Implicatures:
1. ◻(John will come) (Quality)
2. ◻(If John will come, then Mary will come) or
◻(If John will come, then Mary won’t come), and
◻(If John will come, then Bob will come) or
◻(If John will come, then Bob won’t come) (Relation)
3. ◇(Mary will not come), ◇(Bob will not come) (Quantity)
4. ◻(Mary will not come), ◻(Bob will not come) (from 1, 2 & 3)
Finally, we can derive the absense of an exhaustivity implicature in the
following example:
(3) a. Will John come, or Mary?
b. John will come, and maybe Mary too (= ‘or John and Mary’).
Implicatures:
1. ◻(John will come) (Quality)
2. ◇(Mary will come) (Quality)
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3. ◻(If John will come, Mary will come) or
◻(If John will come, Mary won’t come) (Relation)
4. ◇(Mary will not come) (Quantity)
5. ◻(Mary will not come) (from 1, 3 & 4)
In this case, the maxim of relation does not impose any constraints on the
epistemic state, because the response already entails the QUD as such. Traditionally,
the response would have been regarded as ‘canceling’ the exhaustivity
implicature, but I find this terminology misleading; it suggests that the implicature
was first computed, and then later left out. This is not what happens.
The ‘and maybe Mary too’ makes an actual contribution to the literal meaning,
as a consequence of which it entails the QUD and no exhaustivity implicature
is made. 6
4 Expected relatedness
4.1 A more flexible maxim of relation
An utterance can be perfectly fine also if the speaker is not sure whether her
proposal is related (in the sense of entailing the QUD relative to her knowledge
state), but merely expects it to be. Two ways in which relatedness can be
expected are the following:
The speaker has defeasible knowledge that she expects to hold. I.e., she
expects the case under discussion to be not an exception to her rules of
thumb.
The speaker does not have the knowledge herself, but she expects one of
the other discourse participants to provide it. That is, she thinks it is
quite likely distributed knowledge.
In both cases the speaker can be thought of as expecting to know something
(although for sure this is not the only way, and probably not the best way, of
thinking about defeasible knowledge). I will insert the possibility to rely on
expected knowledge explicitly in the maxim of relation:
Definition 8 (Maxim of relation (v2)) Propose a proposition only if it entails
the QUD relative to your knowledge state, or relative to a knowledge state
you expect to enter in the future. The latter must be marked.
How it is marked may be language-dependent. In English, it is marked by risefall-rise
intonation, and optionally by preceding the response with ‘well’ (but
this has other uses, too):
6 The reasoning scheme that leads to an exhaustivity implicature is purely semantic, and
therefore it generalizes to responses to expressions with existential force, and also to some
cases of embedded implicature (Westera, 2012). But instead of discussing such examples here
on a case-by-case basis, I am working on some general facts that will facilitate predictions
regarding natural language, and that should help comparing this pragmatics to the various
exhaustivity operators that have been proposed.
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(4) Will John come to the party?
Well, Mary will go... [rise-fall-rise]
We will investigate several such examples below. In each case, the relation
implicature is computed in the same manner as before, but because it is marked
it will be further embedded under a modal operator, ⊡, that represents the
speaker’s expectations. I do not wish to define a formal semantics for this modal
operator here; an intuitive understanding suffices for the present purposes.
4.2 Expected relatedness implicatures
The following examples show the effect of the updated maxim of relation:
(5) a. Will John come?
b. Well, it will rain. [rise-fall-rise]
Implicatures:
1. ◻(It will rain) (Quality)
2. ⊡(◻(if it rains John will come) or ◻(if it rains John won’t come)
or ◻(if it rains contradiction))
3. ◇(John will come), ◇(John won’t come) (Quantity)
4. ⊡(◻(John will come) or ◻(John won’t come)) (1, 2)
The relation implicature in 2 is computed according to fact 6. It is disjunctive,
because there are different ways to make the utterance entail the QUD. The
third disjunct cannot be the case, for the speaker knows that it is raining.
Of the first two disjuncts, presumably, since people dislike rain, the speaker
expects the latter, but in principle the speaker’s utterance leaves the audience
guessing at what knowledge the speaker expects (indeed, the dialogue can be
very naturally continued with a hearer asking for clarification: ‘okay, so what
do you expect?’). Note that it can be concluded from 1 and 2 together that
the speaker expects to know that John will come, or that he won’t come. The
quantity implicature in 3 of course still holds: neither of the disjuncts in 4 is
certain.
Had the response been unmarked, i.e. pronounced with neutral falling intonation,
the dotted box would have been left out, and the conclusion in 4 would
have directly contradicted the quantity implicatures in 3. Hence, with falling
intonation, the speaker would have violated either the maxim of relation, or the
maxim of quantity. Indeed, these two options are intuitively available to make
sense of such a response: either the speaker violates relation because she wants
to introduce a new, unrelated topic of conversation (i.e., the weather), or the
speaker violates quantity with the purpose of testing the hearer (in which case
the speaker could have appended ‘so what do you conclude?’ to her utterance).
By exactly the same reasoning, rise-fall-rise intonation avoids an exhaustivity
implicature:
(6) a. Will John come, or Mary?
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. Well, John will come. [rise-fall-rise]
Implicatures:
1. ◻(John will come) (Quality)
2. ⊡(◻(if John will come, Mary will come) or
◻(If John will come, Mary won’t come) or
◻(If John will come, contradiction)) (Relation)
3. ◇(Mary will not come) (Quantity)
4. ⊡(◻(Mary will come) or ◻(Mary won’t come)) (1, 2)
In this case, no exhaustivity is implicated for the following reason. Unlike in
example (1), the same dialogue but with normal intonation, here the quantity
implicature in 3 is perfectly compatible with both disjuncts expected in 4,
notably also with the expected knowledge that Mary will come, because the
knowledge is only expected. Therefore, unlike in (1), this possibility cannot be
excluded, and no exhaustivity is implicated.
It seems that counterquestions, too, may rely on defeasible or otherwise
expected knowledge. Obtaining a rise-fall-rise intonation on questions may be
hard, if not impossible, perhaps because it interferes with the default rising
intonation for questions (but I would not be surprised if some kind of marking
is in fact detectible):
(7) a. Will John come?
b. Will it rain?
Implicatures:
1. ◇(it will rain), ◇(it will not rain) (Quality)
2. ⊡(◻(if rain then John) or ◻(if rain then not John), and
◻(if not rain then John) or ◻(if not rain then not John)) (Rel.)
3. ◇(John will come), ◇(John will not come) (Quantity)
4. ⊡(◻(John won’t come) or ◻(John will come iff it rains) or
◻(John will come) or ◻(John comes iff it doesn’t rain)) (1, 2)
This time, the relation implicature is computed according to fact 7. I have omitted
the relation implicatures that have contradictions in them, because each of
those is incompatible with the quality implicature anyway. It follows in 4 that
either the speaker expects there to be a relation between John’s attendance and
the weather, or the speaker expects John to come or not come regardless of the
weather. The latter is a bit counter-intuitive: had the speaker expected this,
why would she have started about the weather? As before, what exactly the
speaker’s defeasible or otherwise expected knowledge is, is left underspecified by
the utterance, and hence inferring it always relies heavily on context. Presumably,
we can rule out that the speaker expects the weather has no bearing on
John’s attendance because, had someone known the answer to the QUD already,
this person would have come forward before the weather was brought up.
Finalizing, recall that each of the above examples can either be read as
involving the speaker’s defeasible knowledge, or as involving the speaker’s expectation
as to what other dialogue participants will be able to tell her. It is
10

easy to think of the latter as involving some kind of request for the other participants
to come forward with this information. At this point, I will leave this
as a mere intuition; but it seems to me worthwile to have a systematic account
of how expectations regarding other participants’ knowledge play a role in the
formation of issues.
4.3 More examples: conditional partial answers
We obtain interesting results if we apply the same reasoning as above, to conditional
partial answers, such as the following:
(8) a. Will John come or not?
b. He’ll come if it’s sunny.
The speaker meaning (at the least) of such responses varies with different intonation
patterns. For instance, it can mean ‘given that it is sunny, he will
come’, and it can suggest a high or low likelihood attached to John’s coming.
Mapping out the different intonations, contexts and speaker meanings is a work
in progress. For now, I will focus on rise-fall-rise intonation, in a context where
it is not known whether it is sunny, and I will ignore any suggestion of high or
low likelihood.
One would expect a conditional answer to raise the issue of whether its
antecedent is true, but as we shall see, only a strengthened biconditional answer
really achieves this. Let us look at the first example.
(9) a. Will John come or not?
b. He’ll come if it’s sunny. [rise-fall-rise]
Implicatures:
1. ◻(s → j) (Quality)
2. ⊡(◻((s → j) → j) (≡ ◻(¬s → j)) and
◻((s → j) → ¬j) (≡ ◻(¬j))) (Relation)
3. ◇(j), ◇(¬j) (Quantity)
4. ⊡(◻(j) or ◻(¬j ∧ ¬s)) (from 1, 2)
Surprisingly perhaps, it is implicated in 2, according to fact 6, that the speaker
expects not ‘it’s sunny’, but rather ‘he’ll come also if it’s not sunny’. Together
with her own knowledge, it entails in 4 that she expects the knowledge that
John will come regardless of the weather, or the knowledge that John won’t
come and (or ‘because’) it’s not sunny. I think both disjuncts would certainly
be fine as responses, and perhaps the predictions of inquisitive pragmatics are
not bad in this respect. But still, one would like the response in (9) about the
weather to somehow lead to a discussion about what the weather is like.
To achieve this, we may assume that the conditional response is strengthened
to a biconditional. Perhaps this is due to interpreting an implication as a causal
statement and applying, as we often do, closed-world reasoning. But regardless
of why exactly it happens, this strengthening is common in conversation, and
we can explore its effect in inquisitive pragmatics:
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(10) a. Will John come or not?
b. He’ll come iff it’s sunny.
Implicatures:
1. ◻(j ↔ s) (Quality)
2. ⊡(◻((j ↔ s) → j) (≡ ◻(¬s → j)) and
◻((j ↔ s) → ¬j) (≡ ◻(s → ¬j))) (Relation)
3. ◇(¬j), ◇(j) (Quantity)
4. ⊡(◻s or ◻¬s)
Here, combining the relation implicature with her own knowledge, the speaker
implicates in 4 that she expects the knowledge that it is sunny or the knowledge
that it is not sunny. Notice that this example is almost the mirror image of
example (7). There, the response was a polar disjunction regarding the weather
(‘will it rain?’), and the implicature was effectively a polar disjunction of biimplications;
here the response itself is a bi-implication, and the implicature is
a polar disjunction regarding the weather.
Finally, for completeness sake, we can explore an ‘only’-conditional in inquisitive
pragmatics:
(11) a. Will John come or not?
b. He’ll only come if it’s sunny.
Implicatures:
1. ◻(j → s) (Quality)
2. ⊡(◻((j → s) → j) (≡ ◻(j)) or
◻((j → s) → ¬j) (≡ ◻(j → ¬s)) (Relation)
3. ◇(¬j), ◇(j) (Quantity)
4. ⊡(◻(j ∧ s) or ◻¬j) (from 1, 2)
As with the normal conditional, the predictions of inquisitive pragmatics are a
bit unexpected, but not downright wrong. It is implicated not that the speaker
expects knowledge about what the weather is like, but rather that she expects
the knowledge that if John comes it won’t be sunny, which, together with the
literal sentence meaning, is a rather cryptic way of saying that the weather
doesn’t matter, that John won’t come anyway. I suspect that plugging in a more
natural form of implication may make the predictions of inquisitive pragmatics
regarding conditional responses more intelligible, and empirically more accurate.
But for the moment, at least the strengthened biconditional works fine already.
Finally, note that with a more neutral intonation (though there seem to
be many variations), for each of the responses the relation implicature will be
incompatible with the quantity implicature. Hence, the responses will have
to be interpreted either as suggesting a new topic for a conversation (flouting
relation), or as intended to test the hearer’s deductive capacities (bypassing
quantity).
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5 Concluding remarks
This is a work in progress. All comments are very much appreciated. My main
aims for the next version will be to prove more general results on the epistemic
constraints imposed by the maxim of relation, in order to make the implicatures
easier to compute for examples that go beyond the ones discussed.
References
Ciardelli, I. (2009). Inquisitive semantics and intermediate logics. (Master
Thesis, University of Amsterdam)
Grice, H. (1975). Logic and conversation. In P. Cole & J. Morgan (Eds.), Syntax
and semantics (Vol. 3, pp. 41–58).
Groenendijk, J., & Roelofsen, F. (2009). Inquisitive semantics and pragmatics.
In J. M. Larrazabal & L. Zubeldia (Eds.), Meaning, content, and argument:
Proceedings of the ILCLI international workshop on semantics,
pragmatics, and rhetoric.
Westera, M. (2012). Meanings as proposals: a new semantic foundation for
gricean pragmatics. (Presented at SemDial 2012)
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