Properties of Intuitionistic Provability and Preservativity Logics

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

Authors
Rosalie Iemhoff
Utrecht University
Dick De De Jongh
University of Amsterdam
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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/jigpal/jzi047
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 42,236
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

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.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

The Fixed Point Property in Modal Logic.Lorenzo Sacchetti - 2001 - Notre Dame Journal of Formal Logic 42 (2):65-86.
On the Beth Properties of Some Intuitionistic Modal Logics.C. Luppi - 2002 - Archive for Mathematical Logic 41 (5):443-454.
[Omnibus Review].Vann McGee - 1991 - Journal of Symbolic Logic 56 (1):329-332.
Closed Fragments of Provability Logics of Constructive Theories.Albert Visser - 2008 - Journal of Symbolic Logic 73 (3):1081-1096.
Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
Provability Logics with Quantifiers on Proofs.Rostislav E. Yavorsky - 2001 - Annals of Pure and Applied Logic 113 (1-3):373-387.
A Course on Bimodal Provability Logic.Albert Visser - 1995 - Annals of Pure and Applied Logic 73 (1):109-142.

Analytics

Added to PP index
2015-02-04

Total views
6 ( #924,908 of 2,254,259 )

Recent downloads (6 months)
3 ( #595,126 of 2,254,259 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature