Introduction

The first chapter discusses why a framework like inquisitive semantics is needed for a satisfactory analysis of information exchange. In particular, it argues that neither declarative nor interrogative sentences can be fully understood in isolation. Further, it is argued that semantic theories which aim to cover both declarative and interrogative sentences should not employ two different notions of semantic content, one for declaratives and one for interrogatives, but should rather be based on a single notion of semantic content that is general enough to capture both the information that sentences convey and the issues that they may raise.This requires a new formal notion of issues, which forms the cornerstone of inquisitive semantics.

Basic operations on propositions

Chapter 3 considers what the basic operations are that can be performed on propositions in inquisitive semantics. In the classical setting, where propositions are simple sets of worlds, one can form the intersection or the union of two propositions, or the complement of a single proposition. These operations play a central role in logic and in semantic analyses of natural languages: conjunction and disjunction are standardly taken to express intersection and union, respectively, while negation is standardly taken to express complementation. It is shown that these operations have natural counterparts in the inquisitive setting, even though propositions are no longer simple sets of worlds.

Propositional attitudes

In Chapter 8 it is shown that inquisitive semantics gives rise to a new view on propositional attitudes, especially those that are relevant for information exchange. Namely, besides the familiar informationdirected attitudes like knowing and believing, it allows us tomodel issuedirected attitudes like wondering and being curious as well. This also leads to a semantic treatment of the verbs that are used to express such attitudes. Among other things, this treatment explains the selectional restrictions of verbs like wonder, i.e. why they only take interrogative complements, while verbs like know take both declarative and interrogative complements.

Disjunction, clause typing, and intonation

This chapter examines how disjunction interacts with clause typing (declarative versus interrogative) and intonation (intonational phrase structure and final pitch contours) in determining the meaning of various kinds of disjunctive sentence types, including disjunctive statements, polar disjunctive questions, open disjunctive questions, and alternative questions. In inquisitive semantics, disjunction is treated uniformly across all these sentence types as expressing the join operator on propositions (or more generally, on all semantic objects of a conjoinable type). It is shown that this treatment, together with an analysis of the semantic contribution of clause type marking and final pitch contours, yields an account of all the relevant constructions.

Conditionals

Chapter 7 argues that inquisitive semantics is not only relevant for questions, but also for statements. The argument is based on recent experimental work on counterfactual conditionals, which shows that even if two premises A and B have exactly the same truth-conditions, the counterfactuals “If A then C” and “If B then C” may have different truth conditions. This means that it is impossible to give a compositional account of counterfactuals based on a purely truth-conditional notion of meaning. On the other hand, the relevant contrast finds a natural explanation once conditionals are analysed in inquisitive semantics. Further benefits of the account are discussed as well: it solves a well-known problem that classical analyses of conditionals have with disjunctive antecedents, and it naturally extends to unconditionals and conditional questions.

Basic notions

Chapter 2 specifies how issues, information states, propositions, and conversational contexts are formally defined in inquisitive semantics. It also defines a number of fundamental relations that may hold between such entities. For instance, it specifies what it means for an information state to resolve an issue or to support a proposition, what it means for a context to be updated with a proposition, and when one proposition entails another.

Questions

Chapter 5 discusses how the meaning of various types of questions in English can be captured in the basic inquisitive semantics framework presented in the previous chapters. Several kinds of questions, including polar questions, alternative questions, and wh-questions, are given a formal analysis. Question coordination and conditional questions are also considered.

Comparison to alternative approaches

Chapter 9 compares inquisitive semantics with some other frameworks which have been proposed for the analysis of questions, in particular with alternative semantics (developed by Hamblin and Karttunen in the 1970s), partition semantics (developed by Groenendijk and Stokhof in the 1980s), and inquisitive indifference semantics (developed by Groenendijk and Mascarenhas in the 2000s). It is argued that inquisitive semantics preserves the essential merits of these previous approaches, while overcoming their main shortcomings. The chapter is also concerned with the division of labor between question semantics and other components of a general theory of interpretation, including a theory of speech acts and discourse pragmatics. It discusses the received view on what the role of a compositional semantic theory of questions should be within such a larger theory of interpretation, and compares it to the one taken in inquisitive semantics, which is argued to be more parsimonious.

Conclusion

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.

A first-order inquisitive semantics

Chapter 4 defines an inquisitive semantics for the language of firstorder logic, which includes the logical connectives (conjunction, disjunction, negation, and implication) as well as universal and existential quantifiers.The semantics of these connectives and quantifiers is given in terms of the algebraic operations on propositions identified in the previous chapter. The main features of the system are highlighted, and illustrated with a range of examples. In Chapters 5–10, a number of linguistic applications of this logical framework are discussed.