Proceedings of the 13 ESSLLI Student Session - Multiple Choices ...

Proceedings of the 13 th ESSLLI Student Session
Thus, φ answers ψ if φ removes some salient possibilities that ψ introduces. This
notion of answerhood should be familiar from a partition theory of questions: in both
cases, answering a question amounts to eliminating some of the possibilities it introduces.
But an important, unique feature of this definition is that an answer doesnt necessarily give
information: it suffices that an answer suggest certain possibilities for the questioner to
consider.
We close this section by working through a few examples. We use the following notational
conventions: {p} = {i ∈ I | i |= p}, {¬p} = {i ∈ I | i �|= p} etc.
Example 2: A Polar Question.
Recall example (2), and let p and q be the propositions ‘Bill is coming to the party’ and ‘John
is coming to the party’ respectively. Let Γ = {I, ∅}; then ⋄p ∧ ⋄q answers ?p ∧ ?q: Γ[?p ∧
?q] = {I, {p}, {¬p}, {q}, {¬q}, ∅} = Γ 1 . Then: Γ 1 [⋄p ∧ ⋄q] = {I, {p}, {q}, ∅} = Γ 2 , and
since 〈Γ 2 〉 ⊂ 〈Γ 1 〉, ⋄p ∧ ⋄q answers ?p ∧ ?q.
Example 3: A Wh-Question.
Consider the question ‘Who is likes to paint?’, and note that ‘Bill might like to paint’ felicitously
answers this question. Let Px be ‘x likes to paint’, and let b be Bill. Let Γ = {I, ∅}.
Then: Γ[?Px] = Γ ∪ {{i | i ≡ j (mod Px)} | j ∈ I }
= Γ ∪ {{i |i(P) = D*}| D* ⊆ D} = Γ 1 . Then
Γ 1 [⋄Pb] = Γ ∪ {{ i | i(P) = D*}[⋄Pb] |D* ⊆ D}
= Γ ∪ {{i | i(b) ∈ i(P) and i(P) = D*}|D* ⊆ D such that i(b) ∈ D*}
Since Γ 1 [⋄Pb] ⊂ Γ 1 , ⋄Pj is an answer to ?Px.
Examples 3 and 4 bring out an important feature of this paper’s framework: epistemic
modals behave much like questions. Both questions and epistemic modals draw attention
to certain possibilities without committing the speaker to a position on whether or not
these possibilities are actual. Epistemic modals, however, are stronger than questions:
modals draw attention to fewer possibilities than questions, suggesting that the chosen
possibilities are somehow more important than the ignored possibilities. The notion of a
salient possibility allows us to represent this similarity between questions and epistemic
modals in fully formal way.
Example 4: Raising Issues Without Questions.
Recall (4), and let p and q be ‘Alice and A are going fishing in Leiden tomorrow’ and ‘It’s
illegal to fish in Leiden’ respectively. Let Γ = {I, ∅}. Then
Γ[p][⋄q] = {{p}, {p ∧ q}, ∅}. Here, since no possibility in Γ[p] satisfied q, the epistemic
modal acted to add the possibility {p ∧ q} to the context. Thus, even though no questions
have been asked in this context, B is able to bring A’s attention to some issue by using an
epistemic modal.
Example 5: Infelicitous Answer.
Responding to a polar question ?φ with ⋄φ ∧ ⋄¬φ should not count as answering the question:
rather, responding to a question with ‘maybe, maybe not’ is a deliberate and almost
reticent refusal to answer the question. Our semantics allows us to account for this: {I,
∅}[?p][⋄p ∧ ⋄¬p] = {I, {p}, {¬p}, ∅}[⋄p ∧ ⋄¬p]
= {I, {p}, {¬p}, ∅}[⋄p][⋄¬p] = {I, {p}, ∅}[⋄¬p] = {I, {p}, {¬p}, ∅}. Thus,
⋄p ∧ ⋄¬p does not answer ?p. Moreover, ⋄p ∧ ⋄¬p is actually equivalent to ?p in this information
state.
In general, ?φ and ⋄φ ∧ ⋄¬φ are equivalent in any information state that is consistent with
both φ and ¬φ, so polar questions can almost be defined using epistemic modals (if we assume
that polar questions presuppose that both of their answers are possible, polar questions
can be defined in terms of the epistemic modality operator).
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