Floris Roelofsen

Inquisitive Semantics: A New Notion of Meaning

This paper presents a notion of meaning that captures both informative and inquisitive content, which forms the cornerstone of inquisitive semantics. The new notion of meaning is explained and motivated in detail, and compared to previous inquisitive notions of meaning.

Algebraic foundations for the semantic treatment of inquisitive content

In classical logic, the proposition expressed by a sentence is construed as a set of possible worlds, capturing the informative content of the sentence. However, sentences in natural language are not only used to provide information, but also to request information. Thus, natural language semantics requires a logical framework whose notion of meaning does not only embody informative content, but also inquisitive content. This paper develops the algebraic foundations for such a framework. We argue that propositions, in order to embody both informative and inquisitive content in a satisfactory way, should be defined as non-empty, downward closed sets of possibilities, where each possibility in turn is a set of possible worlds. We define a natural entailment order over such propositions, capturing when one proposition is at least as informative and inquisitive as another, and we show that this entailment order gives rise to a complete Heyting algebra, with meet, join, and relative pseudo-complement operators. Just as in classical logic, these semantic operators are then associated with the logical constants in a first-order language. We explore the logical properties of the resulting system and discuss its significance for natural language semantics. We show that the system essentially coincides with the simplest and most well-understood existing implementation of inquisitive semantics, and that its treatment of disjunction and existentials also concurs with recent work in alternative semantics. Thus, our algebraic considerations do not lead to a wholly new treatment of the logical constants, but rather provide more solid foundations for some of the existing proposals.

Inquisitive dynamic epistemic logic

Information exchange can be seen as a dynamic process of raising and resolving issues. The goal of this paper is to provide a logical framework to model and reason about this process. We develop an inquisitive dynamic epistemic logic (IDEL), which enriches the standard framework of dynamic epistemic logic (DEL), incorporating insights from recent work on inquisitive semantics. At a static level, IDEL does not only allow us to model the information available to a set of agents, like standard epistemic logic, but also the issues that the agents entertain. At a dynamic level, IDEL does not only allow us to model the effects of communicative actions that provide new information, like standard DEL, but also the effects of actions that raise new issues. Thus, IDEL provides the fundamental tools needed to analyze information exchange as a dynamic process of raising and resolving issues.

Disjunctive questions, intonation, and highlighting

This paper examines how intonation affects the interpretation of disjunctive questions. The semantic effect of a question is taken to be three-fold. First, it raises an issue. In the tradition of inquisitive semantics, we model this by assuming that a question proposes several possible updates of the common ground (several possibilities for short) and invites other participants to help establish at least one of these updates. But apart from raising an issue, a question may also highlight and/or suggest certain possibilities, and intonation determines to a large extent which possibilities are highlighted/suggested.

On the semantics and logic of declaratives and interrogatives

In many natural languages, there are clear syntactic and/or intonational differences between declarative sentences, which are primarily used to provide information, and interrogative sentences, which are primarily used to request information. Most logical frameworks restrict their attention to the former. Those that are concerned with both usually assume a logical language that makes a clear syntactic distinction between declaratives and interrogatives, and usually assign different types of semantic values to these two types of sentences. A different approach has been taken in recent work on inquisitive semantics. This approach does not take the basic syntactic distinction between declaratives and interrogatives as its starting point, but rather a new notion of meaning that captures both informative and inquisitive content in an integrated way. The standard way to treat the logical connectives in this approach is to associate them with the basic algebraic operations on these new types of meanings. For instance, conjunction and disjunction are treated as meet and join operators, just as in classical logic. This gives rise to a hybrid system, where sentences can be both informative and inquisitive at the same time, and there is no clearcut division between declaratives and interrogatives. It may seem that these two general approaches in the existing literature are quite incompatible. The main aim of this paper is to show that this is not the case. We develop an inquisitive semantics for a logical language that has a clearcut division between declaratives and interrogatives. We show that this language coincides in expressive power with the hybrid language that is standardly assumed in inquisitive semantics, we establish a sound and complete axiomatization for the associated logic, and we consider a natural enrichment of the system with presuppositional interrogatives.

Generalized inquisitive logic: completeness via intuitionistic Kripke models

This paper investigates a generalized version of inquisitive semantics (Groenendijk, 2008b; Mascarenhas, 2008). A complete axiomatization of the associated logic is established. The connection with intuitionistic logic is clarified and heavily exploited.

Towards a logic of information exchange: an inquisitive witness semantics

Traditionally, the meaning of a sentence is identified with its truth conditions. This approach is driven by the age-old attention that philosophy has devoted to the study of argumentation. In terms of truth conditions one defines entailment, the crucial notion that rules the soundness of an argument: a sentence ϕ is said to entail another sentence ψ in case the truth conditions for ϕ are at least as stringent as the truth conditions for ψ.

The Interpretation of Prosody in Disjunctive Questions

Alternative questions differ prosodically from identically worded disjunctive yes/no questions in their accentual characteristics and their final pitch contour. Alternative questions are canonically pronounced with a final fall and with pitch accents on all disjuncts, while disjunctive yes/no questions are canonically pronounced with a final rise and generally without pitch accents on every disjunct. This article presents an experiment investigating the importance of these prosodic features in disambiguation. The experiment shows that the final contour is the most informative prosodic feature. Accentual characteristics also play a significant role, but, contrary to what is often assumed in the literature, cannot force an alternative question interpretation or a yes/no question interpretation on their own. Several theories of disjunctive questions are discussed in the light of these experimental results.

Algebraic foundations for inquisitive semantics

Traditionally, meaning is identified with informative content. The central aim of inquisitive semantics [1,2,4,5, a.o.] is to develop a notion of semantic meaning that embodies both informative and inquisitive content. To achieve this, the proposition expressed by a sentence ϕ, [ϕ], is not taken to be a set of possible worlds, but rather a set of possibilities, where each possibility in turn is a set of possible worlds. In uttering a sentence ϕ, a speaker provides the information that the actual world is contained in at least one possibility in [ϕ], and at the same time she requests enough information from other participants to establish for at least one possibility α ∈ [ϕ] that the actual world is contained in α.

Division of Labor in the Interpretation of Declaratives and Interrogatives

This article presents an account of the semantic content and conventional discourse effects of a range of sentence types in English, namely falling declaratives, polar interrogatives and certain kinds of rising declaratives and tag interrogatives. The account aims to divide the labor between compositional semantics and conventions of use in a principled way. We argue that falling declaratives and polar interrogatives are unmarked sentence types. On our account, differences in their conventional discourse effects follow from independently motivated semantic differences combined with a single convention of use, which applies uniformly to both sentence types. As a result, the Fregean ‘illocutionary force operators’ Assertion and Question become unnecessary. In contrast, we argue that rising declaratives and tag interrogatives are marked sentence types. On our account, their conventional discourse effects consist of the effects that are dictated by the basic convention of use that is common to all sentence types considered here, augmented with special effects that are systematically connected to their formal properties. Thus, a central feature of our approach is that it maintains a parallelism between unmarked and marked sentence types on the one hand, and basic and complex discourse effects on the other.