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2017 | OriginalPaper | Buchkapitel

The Dynamic Logic of Stating and Asking: A Study of Inquisitive Dynamic Modalities

verfasst von : Ivano Ciardelli

Erschienen in: Logic, Rationality, and Interaction

Verlag: Springer Berlin Heidelberg

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Abstract

Inquisitive dynamic epistemic logic (IDEL) extends public announcement logic incorporating ideas from inquisitive semantics. In IDEL, the standard public announcement action can be extended to a more general public utterance action, which may involve a statement or a question. While uttering a statement has the effect of a standard announcement, uttering a question typically leads to new issues being raised. In this paper, we investigate the logic of this general public utterance action. We find striking commonalities, and some differences, with public announcement logic. We show that dynamic modalities admit a set of reduction axioms, which allow us to turn any formula of IDEL into an equivalent formula of static inquisitive epistemic logic. This leads us to establish several complete axiomatizations of IDEL, corresponding to known axiomatizations of public announcement logic.

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Most previous presentations of IEL ([3, 8]) use a dichotomous language, in which formulas are divided into two syntactic categories: declaratives and interrogatives. The application of connectives is then subject to syntactic restrictions. Here we follow [4] in using a more general, non-dichotomous language; connectives apply without any restrictions, which leads to a more elegant logic. This difference is not an essential one; the results obtained here can be adapted to the dichotomous setting.

We use the neutral term utterance rather than announcement (used in [8]) because the latter suggests an informational interpretation. E.g., in IDEL, the utterance of a question such as ?p has the effect of raising the issue whether p. This should not be confused with the action of announcing whether p, i.e., announcing the true answer to the question ?p, which is a more standard action of providing information.

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Titel: The Dynamic Logic of Stating and Asking: A Study of Inquisitive Dynamic Modalities
verfasst von: Ivano Ciardelli
Verlag: Springer Berlin Heidelberg
Buch: Logic, Rationality, and Interaction
Print ISBN: 978-3-662-55664-1

Electronic ISBN: 978-3-662-55665-8

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-662-55665-8_17

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