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2015 | OriginalPaper | Buchkapitel

Towards a Suppositional Inquisitive Semantics

verfasst von : Jeroen Groenendijk, Floris Roelofsen

Erschienen in: Logic, Language, and Computation

Verlag: Springer Berlin Heidelberg

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Abstract

One of the primary usages of language is to exchange information. This can be done directly, as in Will Susan sing? No, she won’t, but it is also often done in a less direct way, as in If Pete plays the piano, will Susan sing? No, if Pete plays the piano, Susan won’t sing. In the latter type of exchange, both participants make a certain supposition, and exchange information under the assumption that this supposition holds. This paper develops a semantic framework for the analysis of this kind of information exchange. Building on earlier work in inquisitive semantics, it introduces a notion of meaning that captures informative, inquisitive, and suppositional content, and discusses how such meanings may be assigned in a natural way to sentences in a propositional language. The focus is on conditionals, which are the only kind of sentences in a propositional language that introduce non-trivial suppositional content.

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Fußnoten
1
See Ciardelli (2009); Groenendijk and Roelofsen (2009); Ciardelli and Roelofsen (2011) for early expositions of InqB, and Roelofsen (2013); Ciardelli et al. (2013) for a more recent perspective and comparison with earlier work on the semantics of questions (e.g., Hamblin 1973; Karttunen 1977; Groenendijk and Stokhof 1984).
 
2
One way to reject the proposal expressed by (1a), not listed above, is as follows:
(i) No, if Pete plays the piano, Susan might not sing.
This response involves the epistemic modal might. Accounting for such responses is beyond the scope of the current paper, but not beyond the scope of InqS in general. Indeed, the InqS analysis of epistemic modals presented in Aher 2014 naturally characterizes (i) as a rejecting response to (1a), and also clearly brings out the difference between (i) and (1b). Namely, (i) rejects (1a) in a defeasible way, subject to possible retraction when additional information becomes available, while (1b) rejects (1a) indefeasibly. Or, phrased in terms of conversational attitudes, (i) signals that the addressee is unwilling to accept the proposal expressed by (1a), while (1b) signals that she is really unable to do so.
There is a rich psycholinguistic literature on the denial of conditional statements (see, e.g., Handley 2006; Espino and Byrne 2012; Égré and Politzer 2013, and references therein), but the distinction between defeasible and indefeasible rejection has, to the best of our knowledge, not been brought to attention previously.
 
3
The need to specify both support and reject conditions is independent from the need to have a notion of meaning that embodies inquisitive content. There is a lot of work addressing the first issue while leaving inquisitive content out of the picture, e.g., work on data semantics (Veltman 1985), game-theoretic semantics and independence friendly logic (Hintikka and Sandu 1997; Hodges 1997), dependence logic (Väänänen 2007), and truth-maker semantics (Fraassen 1969; Fine 2012).
 
4
In terms of the three basic semantic notions, a whole range of derived semantic notions can be defined, which can be used in the same way to define additional logical responsehood relations. One case in point is the notion of a state \(s\) suppositionally dismissing a sentence \(\varphi \), which holds when \(s\) dismisses a supposition of \(\varphi \), and no substate of \(s\) supports or rejects \(\varphi \). For lack of space, a proper discussion of these logical responsehood relations has to be left for another occcasion.
 
5
This notion of supposability preserves a key property of the simple notion of supposability in terms of consistency, namely that for every support-alternative \(\alpha \) of any sentence \(\varphi \), there is a unique ‘turning point’ state \(s\), such that \(\alpha \) is supposable in any superstate of \(s\) and no longer supposable in any substate of \(s\). For this to obtain, it is crucial that the notion requires support to be preserved in all states between \(\alpha \) and \(s\cap \alpha \), and not just in \(s\cap \alpha \).
 
6
Recall from our discussion in Sect. 3.1 that the fact that we are considering a propositional language based on a finite set of atomic sentences is crucial in ensuring that every state that supports a sentence is contained in an alternative for that sentence, which in turn justifies our formulation of the clauses for implication in terms of alternatives. However, this cannot always be ensured. For instance, if we consider a first-order language with an infinite domain of interpretation, the existence of alternatives can no longer be guaranteed (Ciardelli 2009). Fortunately, there is a way to formulate the clauses for implication that does not make reference to alternatives, and which in the current setting is equivalent to the clauses as formulated in Definition. 6:
  • \(s~\models ^{+}\varphi \rightarrow \psi \) iff \([\varphi ]^+\ne \emptyset \) and \(\forall t\in [\varphi ]^+\exists u\supseteq t\in [\varphi ]^+\): \(s\lhd u\) and \(s\cap u~\models ^{+}\psi \)
  • \(s~\models ^{-}\varphi \rightarrow \psi \) iff \([\varphi ]^+\ne \emptyset \) and \(\exists t\in [\varphi ]^+\forall u\supseteq t\in [\varphi ]^+\): \(s\lhd u\) and \(s\cap u~\models ^{-}\psi \)
  • \(s~\models ^{\circ }\varphi \rightarrow \psi \)  iff \([\varphi ]^+=\emptyset \) or    \(\exists t\in [\varphi ]^+\forall u\supseteq t\in [\varphi ]^+\): \(s\vartriangleleft \!\!\!\!/\,\,u\) or   \(s\cap u~\models ^{\circ }\psi \)
.
 
7
Sentence (22d) not only dismisses a supposition of the other three sentences, but it suppositionally dismisses them, given the way this notion was defined in footnote 4.
 
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Metadaten
Titel
Towards a Suppositional Inquisitive Semantics
verfasst von
Jeroen Groenendijk
Floris Roelofsen
Copyright-Jahr
2015
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-46906-4_9