## Ivano Ciardelli, Jeroen Groenendijk, and Floris Roelofsen

Print publication date: 2018

Print ISBN-13: 9780198814788

Published to Oxford Scholarship Online: December 2018

DOI: 10.1093/oso/9780198814788.001.0001

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# Conclusion

Chapter:
(p.193) 10 Conclusion
Source:
Inquisitive Semantics
Publisher:
Oxford University Press
DOI:10.1093/oso/9780198814788.003.0010

# Abstract and Keywords

The concluding chapter provides a summary of the architecture of the framework presented in the book, emphasizing its modular nature. It argues that the high-level desiderata discussed in Chapter 1 have been met. The framework provides a formal notion of issues that allows for a suitable representation of semantic content, conversational contexts, and propositional attitudes. In particular, it makes an integrated treatment of declarative and interrogative sentences possible, with a single notion of semantic content which is general enough to deal with both sentence types at once, rather than a separate notion of content for each sentence type.

We will end with an overview of the main concepts that play a role in the framework we presented, emphasizing its modular architecture. After that, we will return to the high-level desiderata discussed in Chapter 1 and consider to what extent they have been met.

# 10.1 Overview of main concepts

Figure 10.1 provides an overview of the main concepts that play a role in InqB, the basic inquisitive semantics system presented in Chapter 4, and the dependencies between them. InqB assumes a particular logical language Ł, namely the language of standard first-order logic (the upper leftmost item in the diagram). Given this language, we defined the models relative to which the sentences in our language would be interpreted. A model was construed as a set of possible worlds W, associated with a domain of discourse and an interpretation function determining the denotation of the basic elements of our language (function symbols and relation symbols) in each possible world. Thus, a model determines a certain logical space, the set of worlds W, as well as a particular connection between the worlds in this space and the basic elements of the language under consideration.

We adopted the standard notion of information states as sets of possible worlds, i.e., subsets of W. In terms of information states, we defined a new notion of issues, and based on this notion of issues we introduced a notion of propositions encompassing both informative and inquisitive content. We defined a notion of entailment between propositions, and characterized two kinds of semantic operators on propositions: (i) algebraic operators, which for instance yield the meet or the join of two propositions with regard to entailment, and (ii) projection operators, which trivialize either the informative or the inquisitive content of a given proposition. Finally, based on these semantic operators, (p.194) we defined a semantics for the language Ł that we started out with, coming full circle.

Figure 10.1 Dependency diagram of the main concepts in InqB.

Having laid out this schematic overview of InqB, we would like to emphasize that all the notions which play a crucial role in this system, except for the logical language and the models with respect to which the sentences in the language are interpreted, were already characterized in Chapters 2–3, without reference to any particular logical or natural language. This makes these notions highly general and widely applicable.

As we saw in Chapter 4, what becomes necessary when turning to a particular language is a more specific characterization of the assumed logical space. In Chapters 2–3, we just assumed a generic set of possible worlds W as our logical space, without any further specification. The moment we fix a particular logical language, we have to establish a connection between the worlds in our logical space and the basic elements of our language. Thus, in Chapter 4, we supplemented the set of possible worlds W with a domain of individuals D and a function I determining the denotation of the basic elements of our language (in this case, function symbols and relation symbols) with regard to each world wW. Having fixed this connection between ‘worlds and words’, all the general notions introduced in Chapters 2–3 could be imported straightforwardly.

In Chapter 8 we considered an extension of InqB with modal operators to describe the knowledge and issues of a given set of agents. Accordingly, we equipped our logical space with a set of state maps$ΣA$, determining the information states and inquisitive states of all the agents at every world. Having thus equipped the possible worlds in our logical (p.195) space with the structure needed to interpret our extended language, all the general notions laid out in Chapters 2–3 could once again be imported straightforwardly.

The fact that the framework is built up in this modular way makes it very flexible. There are many ways in which the basic notions introduced here may be further refined, extended, and applied (see Further Reading for some references).

# 10.2 Mission accomplished?

Let us now return to the high-level desiderata discussed in Section 1.2, and assess to what extent the framework we presented addresses these desiderata.

The first high-level desideratum was a formal notion of issues that allows for a suitable representation of semantic content, conversational contexts, and propositional attitudes. In Chapter 2 we introduced such a notion of issues, and in terms of it we defined new notions of semantic content (propositions), conversational contexts, and context update. In Chapters 5, 6, and 9 we argued that the new notion of semantic content is particularly suitable for the analysis of questions, overcoming the main shortcomings of previous frameworks for question semantics (alternative semantics, partition semantics, and indifference semantics). In Chapter 8 we showed that the new notion of issues facilitates a richer view on propositional attitudes as well, encompassing both information-directed attitudes like know and issue-directed attitudes like wonder.

The second high-level desideratum was a framework that allows for an integrated treatment of declarative and interrogative sentences, with a single notion of semantic content which is general enough to deal with both sentence types at once, rather than a separate notion of content for each sentence type. One argument we made to justify this desideratum was that declarative and interrogative sentences are to a large extent built up from the same lexical, morphological, and intonational elements. A general characterization of the semantic contribution of each of these elements should capture both their contribution to the informative content and to the inquisitive content of the sentence that they are part of. This requires a framework in which the semantic content of a sentence—the proposition it expresses—encompasses both informative and inquisitive content.

(p.196) The notion of propositions introduced in Chapter 2 satisfies this requirement, and the merits of this feature of the framework were illustrated most explicitly in Chapter 6 with an analysis of declarative and interrogative sentences involving disjunction and various intonation patterns. Both disjunction and the relevant intonational elements were given a uniform treatment across various sentence types. Another important result of the approach was discussed in Chapter 7: while originally intended to broaden the domain of logical semantics from declaratives to interrogatives, we have seen that it also leads to an improved analysis of declaratives as such. We illustrated this point in the domain of conditionals, whose truth-conditions are sensitive to the inquisitive content of their antecedent.

Thus, both desiderata have been met and the ensuing benefits have been concretely substantiated. From a narrow perspective, then, our goals have been achieved. From a broader perspective, however, these results just indicate that our general mission is worthwhile pursuing. We do not see the basic framework presented here as a final product but much rather as a point of departure.