Draft:Question semantics

Question semantics is the linguistic study of the meaning of questions and answers. Questions are a major area of research in the syntax-semantics interface.


 * Play as important of a role in semantics as they do in syntax.
 * what else should go in this paragraph?

Overview
Questions are a major topic of research in formal semantics because they do not fit with the classic view of denotations as truth conditions. An influential approach developed by Charles Hamblin and Lauri Karttunen defines the meaning of a question as the set of possible answers to that question.

What is a question?
Dayal .... speech act:


 * Speaker S questions Hearer H about proposition $$p$$ if and only if:

1. S does not know whether $p$ is true or false

2. S wants to know whether $p$ is true or false

3. S believes H knows the answer of $p$.

Polar questions
A polar question (or yes-or-no question) is a question that asks whether a given proposition is true. For instance, the following English example can be answered with "yes" or "no", indicating whether or not Igor wrote a poem


 * 1) Did Igor write a POEM?
 * a. Yes (Igor wrote a poem)
 * b. No (Igor did not write a poem)
 * i. No, Igor wrote a book.
 * 1) Did Igor WRITE a poem?
 * a. Yes (Igor wrote a poem)
 * b. No (Igor did not write a poem)
 * i. No, Igor read a poem.
 * 1) Did IGOR write a poem?
 * a. Yes (Igor wrote a poem)
 * b. No (Igor did not write a poem)
 * i. No, John wrote a poem.

Alternative questions
An alternative question is a question that asks which of several possibilities is true. For instance, the following English example can be answered with "a poem", "a book", but not with "yes" or "no". In this data sentence, the symbols "↑" and "↓" mark a rising and falling intonation contours respectively.


 * 1) Did Igor write a POEM↑ or a BOOK↓? (alternative question)

Alternative questions are generally constructed using disjunction. However, additional ingredients such as focus, intonation, and particles are often necessary to distinguish them from other kinds of questions.


 * 1) Did Igor write [a POEM or a BOOK]↑? (polar question)

Conditional questions
Conditional questions are questions embedded in the consequent of a conditional. Conditional questions can be indicative or counterfactual as shown by the English examples below.


 * 1) If Rebecca paints her car, what color would she have painted it?
 * 2) If Rebecca had painted her, what color would she have painted it?

Embedded questions
Questions can be embedded under propositional attitudes, speech reports, and other embedding predicates.


 * 1) Maria knows whether Joel is coming to the party.
 * 2) Maria knows whether Joel or Lisa is coming to the party.
 * 3) Maria knows who is coming to the party.
 * 4) Maria asked Martin where one can buy an Italian newspaper in Amsterdam.
 * 5) Maria told Martin where one can buy an Italian newspaper in Amsterdam.

Hamblin semantics
Alternative semantics is a framework in which expressions denote alternative sets, understood as sets of objects of the same semantic type. In the original version of the proposal, developed by Charles Leonard Hamblin in 1973, a question denotes the set of its possible answers. Thus, if $$P$$ and $$Q$$ are propositions, then $$\{P,Q\}$$ is the denotation of the question whether $$P$$ or $$Q$$ is true. In a notable modification proposed by Lauri Karttunen, this idea was revised so that a question denotes the set of its true answers at the world of evaluation.

Inquisitive semantics
Inquisitive semantics is a framework for question semantics which follows Hamblin in treating questions denotations as sets of propositions. However, it departs from Hamblin semantics in two fundamental ways. First, it is more restrictive in that it requires that denotations be nonempty and downward closed. For example, where Hamblin semantics would posit a denotation containing only the two propositions $$P$$ and $$Q$$, inquisitive semantics would posit a denotation containing those propositions and all of their subsets. Second, inquisitive semantics attributes denotations of this sort to all expressions, not just question-denoting ones. For example, where Hamblin semantics would follow traditional semantics in assigning a declarative clause the denotation $$P$$, inquisitive semantics would assign it the set containing $$P$$ and all of its subsets.

History
Charles Hamblin