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Glivenko's theorem, finite height, and local tabularity
Glivenko's theorem states that a formula is derivable in classical
propositional logic iff under the double negation it is derivable
in intuitionistic propositional logic :
iff . Its analog for the modal logics
and states that iff
. In Kripke semantics,
is the logic of partial orders, and is the logic of
partial orders of height 1. Likewise, is the logic of preorders,
and is the logic of equivalence relations, which are preorders of
height 1.
In this paper we generalize Glivenko's translation for logics of arbitrary
finite height