Glivenko Theorems for Substructural Logics over FL

Journal of Symbolic Logic 71 (4):1353 - 1384 (2006)
It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part of the paper, we also discuss some extended forms of the Kolmogorov translation and we compare it to the Glivenko translation
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/27588518
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 15,879
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

No references found.

Add more references

Citations of this work BETA
Hiroakira Ono (2009). Glivenko Theorems Revisited. Annals of Pure and Applied Logic 161 (2):246-250.

Add more citations

Similar books and articles
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Greg Restall (forthcoming). Substructural Logics. Stanford Encyclopedia of Philosophy.
Norihiro Kamide (2002). Kripke Semantics for Modal Substructural Logics. Journal of Logic, Language and Information 11 (4):453-470.
Greg Restall (1930). Models for Substructural Arithmetics. Australasian Journal of Philosophy 8:82-99.

Monthly downloads

Added to index


Total downloads

17 ( #156,877 of 1,725,158 )

Recent downloads (6 months)

1 ( #349,161 of 1,725,158 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.