A generalized notion of weak interpretability and the corresponding modal logic
type: Item
instance of: scholarly article
title: A generalized notion of weak interpretability and the corresponding modal logic
zbMATH Open document ID: 0791.03032
DOI: 10.1016/0168-0072(93)90201-N
author: Giorgie Dzhaparidze
published in: Annals of Pure and Applied Logic
publication date: 1993-09-22T00:00:00Z
review text: The paper introduces two interpretability-style relations between theories: tolerance (generalized weak interpretability) and cointerpretability. Intuitively, \(S\) is tolerant with \(T\) if \(T\) can be translated into \(S\) in such a way that the translation of any theorem of \(T\) is consistent with \(S\); and \(S\) cointerprets \(T\), if \(S\) can be translated into \(T\) in such a way that \(S\) proves every formula the translation of which is a theorem of \(T\). The set of all valid principles of tolerance is modal-logically axiomatized and its decidability is proven. As for cointerpretability, it turns out to be a characterization of sigma-one conservativity (over strong theories) in terms of translations.
Mathematics Subject Classification ID: 03F30
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03F25
zbMATH DE Number: 416884
zbMATH Keywords: provability
zbMATH Keywords: generalized weak interpretability
zbMATH Keywords: tolerance
zbMATH Keywords: cointerpretability
zbMATH Keywords: decidability
zbMATH Keywords: sigma-one conservativity
MaRDI profile type: Publication
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Wikidata QID: Q55952401
DBLP publication ID: journals/apal/Dzhaparidze93
description: scientific article; zbMATH DE number 416884