Notre Dame Journal of Formal Logic

Questions and Dependency in Intuitionistic Logic

Ivano Ciardelli, Rosalie Iemhoff, and Fan Yang

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Abstract

In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of statements, and added formulas expressing questions and dependencies to this classical core. In this paper, we broaden the scope of these investigations by studying questions and dependency in the context of intuitionistic logic. We propose an intuitionistic team semantics, where teams are embedded within intuitionistic Kripke models. The associated logic is a conservative extension of intuitionistic logic with questions and dependence formulas. We establish a number of results about this logic, including a normal form result, a completeness result, and translations to classical inquisitive logic and modal dependence logic.

Article information

Source
Notre Dame J. Formal Logic, Volume 61, Number 1 (2020), 75-115.

Dates
Received: 6 April 2017
Accepted: 24 January 2019
First available in Project Euclid: 18 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1576638403

Digital Object Identifier
doi:10.1215/00294527-2019-0033

Mathematical Reviews number (MathSciNet)
MR4054246

Subjects
Primary: 03B65: Logic of natural languages [See also 68T50, 91F20]
Secondary: 03B60: Other nonclassical logic 03B20: Subsystems of classical logic (including intuitionistic logic)

Keywords
inquisitive logic dependence logic team semantics intuitionistic logic

Citation

Ciardelli, Ivano; Iemhoff, Rosalie; Yang, Fan. Questions and Dependency in Intuitionistic Logic. Notre Dame J. Formal Logic 61 (2020), no. 1, 75--115. doi:10.1215/00294527-2019-0033. https://projecteuclid.org/euclid.ndjfl/1576638403


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