Properties of Intuitionistic Provability and Preservativity Logics

Logic Journal of the IGPL 13 (6):615-636 (2005)
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Abstract

We study the modal properties of intuitionistic modal logics that belong to the provability logic or the preservativity logic of Heyting Arithmetic. We describe the □-fragment of some preservativity logics and we present fixed point theorems for the logics iL and iPL, and show that they imply the Beth property. These results imply that the fixed point theorem and the Beth property hold for both the provability and preservativity logic of Heyting Arithmetic. We present a frame correspondence result for the preservativity principle Wp that is related to an extension of Löb's principle

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Author Profiles

Rosalie Iemhoff
Utrecht University
Dick De De Jongh
University of Amsterdam

Citations of this work

Provability logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.
On Geometric Implications.Amirhossein Akbar Tabatabai - forthcoming - Studia Logica:1-30.
Avicenna on Syllogisms Composed of Opposite Premises.Behnam Zolghadr - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 433-442.

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References found in this work

Interpolation, Definability and Fixed Points in Interpretability Logics.Carlos Areces, Eva Hoogland & Dick de Jongh - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 53-76.

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