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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - QuModQu (Quantification and modality in the realm of questions)

Teaser

Summary

The interpretation of linguistic expressions has been investigated from various theoretical perspectives, ranging from linguistics and philosophy to logic and cognitive science, leading to many applications in computer science. At the heart of this enterprise is a simple yet powerful notion of meaning as truth-conditional content. Despite its merits, this view has a fundamental limitation: while suitable for statements, it does not apply to other sentence types, like questions.

This limitation has recently led the PI and his collaborators to propose a more general notion of meaning, giving rise to a new semantic framework called inquisitive semantics. This framework opens up new horizons for all disciplines concerned with linguistic meaning. The present project explores these horizons in logic and linguistics, also making substantial connections with philosophy and computer science.

In linguistics, besides providing a framework for the analysis of questions, the new approach suggests that inquisitive content plays a role in the semantics of statements as well, which sheds new light on recent linguistic observations that are highly puzzling from a purely truth-conditional point of view.
In logic, the enriched notion of meaning also opens up new, exciting possibilities. While logic is standardly concerned with reasoning processes that involve concrete pieces of information, our new perspective also allows us to consider reasoning processes involving types of information. Relations between types of information play a central role in natural sciences, and also in various applicative domains in computer science.

The project explores in detail how the inquisitive perspective extends the boundaries of logic and linguistics, with a particular focus on the domains of quantification and modality, which are central to both enterprises. The approach is highly inter-disciplinary in nature, forging cross-fertilization between the two fields.

Work performed

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Subproject 1: Modality in Language
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Core achievements:
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- P1: A new general notion of modality, which encompasses both \"\"believe\"\"-type modals and \"\"wonder\"\"-type modals, and a general semantic explanation for the fact that these modals only take one type of complement, declarative or interrogative (Theiler et al, 2019).
- P2: A new treatment of \'hybrid\' modal expressions like \"\"know\"\", which take both declarative and interrogative complements (Theiler et al, 2018).
- P4: Experimental evidence that counterfactual conditionals are sensitive to the inquisitive content of their antecedent (Ciardelli et al, 2018).

Additional achievements, not anticipated in the project proposal:
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- A new theory of distributive ignorance inferences with \"\"believe\"\" and \"\"wonder\"\" (Cremers et al, 2018).

Main output:
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A uniform semantics for declarative and interrogative complements.
Nadine Theiler, Floris Roelofsen, and Maria Aloni. Journal of Semantics 35(3), pp. 409â€“466, 2018.

Picky predicates: why \"\"believe\"\" doesn\'t like interrogative complements, and other puzzles
Nadine Theiler, Floris Roelofsen, and Maria Aloni. Natural Language Semantics. Published online March 2019.

Distributive ignorance inferences with \"\"wonder\"\" and \"\"believe\"\"
Alexandre Cremers, Floris Roelofsen, and Wataru Uegaki. To appear in Semantics and Pragmatics, accepted September 2018.

Two switches in the theory of counterfactuals
Ivano Ciardelli, Linmin Zhang and Lucas Champollion. Linguistics and Philosophy 41(6), pp. 577â€“621, 2018.

Subproject 2: Quantification in Language
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Core achievements:
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- P1: Experimental evidence on how different types of quantifiers propagate inquisitive content.
- P2: A new theory of ignorance implicatures of modified numerals (Coppock et al, 2018) and an experimental assessment of this theory (Cremers et al, 2019).
- P3: An initial analysis of \"\"quexistentials\"\": words that can serve both as existential quantifiers and question words (Hengeveld et al, 2018).
- P4: An initial analysis of NPIs in questions (Roelofsen, 2018).

Additional achievements:
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- Experimental evidence for the polarity-sensitivity of certain question embedding predicates (van Gessel et al, 2018).

Main output:
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Pair-list interpretations of questions with quantifiers
Thom van Gessel, Alexandre Cremers and Floris Roelofsen. Presented at PALLMYR, 2017.

Implicatures of modified numerals: quality or quantity?
Liz Coppock, Ivano Ciardelli, and Floris Roelofsen. Proceedings of Sinn und Bedeutung, 2017.

Ignorance implicatures of modified numerals
Alexandre Cremers, Liz Coppock, Jakub Dotlacil, and Floris Roelofsen. Submitted, 2019.

Quexistentials, Part I
Kees Hengeveld, Sabine Iatridou, and Floris Roelofsen. Presented at an MIT, 2018.

NPIs in questions
Floris Roelofsen. Colloquium at NYU, 2018.

Polarity sensitivity of question embedding: experimental evidence
Thom van Gessel, Alexandre Cremers, and Floris Roelofsen. SALT 28, pp. 217-232, 2018.

Subproject 3: Quantification in Logic
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Core achievements:
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- P1: Important model-theoretic results on first-order inquisitive logic (Grilletti 2018) and on the expressive power of the logic (Ciardelli and Grilletti, to appear).
- P2: An axiomatisation for several large fragments of the logic (not submitted yet).

Additional achievements:
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- Two articles containing general arguments in favor of the logical analysis of questions that we are proposing, including detailed comparisons with prominent previous approaches (Ciardelli 2017, 2018).

Main output:
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Disjunction and Existence Properties in Inquisitive First-Order Logic
Gianluca Grilletti, Studia Logica, published online October 201\"

Final results

All the results listed above go beyond the state of the art in logic and linguistics, and build towards an integrated theory of the interaction between questions, modality and quantification.

The progress made so far is in line with our expectations at the outset of the project. In some cases we obtained new insights that we had not anticipated, but overall the results seem to lead to a coherent picture in line with what we had sketched in the proposal.
We are confident that we will be able to address the remaining questions formulated in the proposal during the second half of the project.