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JSYML
2006

Glivenko theorems for substructural logics over FL

13 years 11 months ago
Glivenko theorems for substructural logics over FL
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.
Nikolaos Galatos, Hiroakira Ono
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JSYML
Authors Nikolaos Galatos, Hiroakira Ono
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