Properties of Intuitionistic Provability and Preservativity Logics

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

Rosalie Iemhoff
Utrecht University
Dick De De Jongh
University of Amsterdam
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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DOI 10.1093/jigpal/jzi047
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Interpolation, Definability and Fixed Points in Interpretability Logics.Carlos Areces, Eva Hoogland & Dick de Jongh - 2000 - In Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 2. CSLI Publications. pp. 53-76.

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