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A Modal Interpretation of the Logic of Interrogation

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Abstract

We propose a novel interpretation of natural-language questions using a modal predicate logic of knowledge. Our approach brings standard model-theoretic and proof-theoretic techniques from modal logic to bear on questions. Using the former, we show that our interpretation preserves Groenendijk and Stokhof's answerhood relation, yet allows an extensional interpretation. Using the latter, we get a sound and complete proof procedure for the logic for free. Our approach is more expressive; for example, it easily treats complex questions with operators that scope over questions. We suggest a semantic criterion that restricts what natural-language questions can express. We integrate and generalize much previous work on the semantics of questions, including Beck and Sharvit's families of subquestions, non-exhaustive questions, and multi-party conversations.

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Authors and Affiliations

  1. Division of Engineering and Applied Sciences, Harvard University, 33 Oxford Street, Cambridge, MA, 02138, USA

    Rani Nelken & Chung-Chieh Shan

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  1. Rani Nelken
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  2. Chung-Chieh Shan
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Correspondence to Chung-Chieh Shan.

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Nelken, R., Shan, CC. A Modal Interpretation of the Logic of Interrogation. JoLLI 15, 251–271 (2006). https://doi.org/10.1007/s10849-005-9012-8

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  • DOI: https://doi.org/10.1007/s10849-005-9012-8

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