We are interested in explaining the above pattern. We will claim that in case of wh-questions this has to do with redundancy of the questions in the utterance context. If we want to provide an explanation along these lines we will have to make use of a discourse model which allows us to precisely formulate the notion of redundancy we have in mind. But the use of a discourse model is not only motivated by that. We are dealing with pairs of sentences. And, the meaning of the first sentence in this pair evidently influences the acceptability of the second sentence. If we want to capture this we need at least a crude model of the dynamics between these sentences, that is in how far the meaning of one sentence influences the context in a way that another sentence may or may not be accepted by the context after the first sentence got integrated in the context. The data thus presents itself in a way suggesting that the facts are related to discourse properties (at least in some cases).
6.3.1
A simple discourse model
A contextC can be seen as comprising different kinds of information: it comprises the information of what was said, what i factual information, and which issues are still open, and many other kinds of information (I can reference Krifka here). In the basic inquisitive system InqB, a context Cis seen as a proposition (add reference to LN). This, together with an appropriate context update operation, provides a very simple model of discourse dynamics.
Unfortunately, this won’t do for us. LetC be a context in the sense of InqB. Since we have two meaning components – presupposition vs at-issue information – we need a slightly more involved update function than in InqB (where we can get away with set-theoretic intersection ⋂). Let us further assume that the update proceeds as follows: we first check whether the presuppositions of the proposition we wish to update our context C with are satisfied in the context. If so, we proceed with checking for the at-issue content, if not, no update takes place (presupposition failure).
Now consider the following discourse:
(81) a. Mary smokes.
b. Does JohnF smoke too?
Given C we will first try to update with (81-a). (81-a) imposes no restrictions on the presuppositions on the states in C and so the presupposition check is trivially satisfied. We next check whether the at-issue information is satisfied in the context by which we may mean that we check for some states in C whether they satisfy the at-issue information. Technically, we may conceive of this as (i) checking whether for each
πs for eachs∈ C we have thatπs satisfies the presuppositions in question, and (ii) intersecting the at-issue information ofC with the at-issue information of the proposition in question – so, the InqB update.
Imagine now we updated successfully. We will then proceed in the same manner for (81-b). But, we will not make it pass the presuposition check. The reason is that since (81-a) does not impose any restrictions on the presuppositions of the states inC, we will in general not have that the presupposition of (81-b) is met inC. The update procedure stops. What we need is a different model, in particular we need different contexts. We will model a contextCLas a non-empty downward closed set of sets of world-assignment pairs relative
to the logical space L. Furthermore, we will define the following update operation:4
Definition 6.3.1. (Context update operation,⊓) LetC be a context, andP a proposition.
C ⊓P∶=⎧⎪⎪⎪⎨⎪⎪
⎪⎩
C ∩ {α∣∃π∶ ⟨π, α⟩ ∈P} if for all α∈ C ∶ ∃s∈P, πs=α
undefined otherwise
So, we are checking first whether for all sets of possibilitiesαinC, whether there is some statesin the propositionP denoted by the sentenceSsuch thatαis identical to the presuppositionπsof the states. This boils down to checking whether the presupposition of the proposition P is satisfied in the contextC. Hence, a sentence can only update a context if the presupposition of the proposition denoted by the sentence holds
4Unfortunately, the discourse pragmatics are not spelled out in the handout of Champollion et al. (2017) and so we cannot
throughout the state. This restriction is important. If we would update without any reservations we would possibly end up in a context C′ that no longer contains the actual state.
The second step consists in updating the context. We update the contextC by intersecting it with the set of all sets of possibilities α, such that for some set of possibilities πwe have that ⟨π, α⟩ is a state inP. This boils down to saying that we update with any at-issue content of a state for which we also find that the presupposition of it is satisfied.
In case the presupposition check fails, the update procedure halts and no update takes place. This is the “undefined” case.
This is motivated by our notion of state itself. The presupposition component is conceived of as the restriction under which the context is updated with the at-issue content (ref champollion et al.). The above makes this idea formally precise.
Unfortunately, the proposed update model comes with a build in problem. Imagine we are discourse initial. Nothing has been said yet, nothing settled, etc. The logical space has not yet been reduced in its entirety. In that case we may take C = ℘(L). When now asking a wh-question such as “Who smokes?” we will not update, for the presupposition of the question is not a superset of all subsets of L. In particular, we have that the presupposition of the question is a proper subset of L as made clear in the figure below. Technically, this is unproblematic, but conceptually it is. It has been argued by many scholars that discourse is not simply a (linear) process that is supposed to narrow down our uncertainty about what the world is, but it underlines constraints about how to do so. In particular, it has been argued thatquestions organize discourse in discrete steps and that assertions need to address the questions in order to be felicitous in the discourse (to be a propermove) (cf. Katzir and Singh (2015) and the references therein) Being sympathetic with this picture, we do not want to make use of the above model.
Instead, we will propose and make use of the model below. The idea comes from the following picture: a proposition in both Champollion et al. (2017) and in CRISP can be thought of as a list of offerings. When uttering a sentence, we propose a list to the discourse participants from which they are supposed to choose an item. The items are – in a sense – classical propositions (which come with a presupposition and an assertion). Alternatively, they may reject the list as such (presupposition denial, etc.). Usually, when we offer others something from a list, the items on the list are supposed to be available to them. Bringing this idea down to CRISP, we can think of the items as the alternatives and their substates of the proposition. What we then want is that each alternative can update the context. Hence, what we need to check is whether for each alternative the context is such that we can update it with a substate of it. The latter part comes from the notion of meaning used in inquisitive semantics.
We are now in a position to define the notions of support and redundancy:
Definition 6.3.2. (support)
Let C be a context and let P be a proposition. We say thatP is supported by context C if we have that C ⊓P≠ ∅. We writeC ⊢P in that case.
Definition 6.3.3. (redundancy) Let P be a proposition. We say: 1. P is redundant in context CifC ⊓P= C
2. forP an inquisitive proposition,P is redundant in contextCif∃s[s∈Alt(P) ∧ ∀α∈ C ⊓P[∃s′⊑s[α
s′=
The case in 1. corresponds to the situation where P was already issued, as for instance in “A: Who smokes? B: Mary. C: Who smokes?” The question issues by A′is redundant in that case.
The case in 2., on the other hand, corresponds to the situation where a question is issued but the context is such that it is already resolved. This is the case above: B’s utterance resolves C’s question already.