VF is a new very weak subintuitionistic logic, sound and complete for adapted Fitting–Marek–Truszczyński frames, strictly weaker than WF, with disjunction and finite-frame properties and modal companions.
Proof analysis in intermediate logics.Archive for Mathematical Logic, 51(1-2):71–92, February 2012
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Very weak subintuitionistic logics
VF is a new very weak subintuitionistic logic, sound and complete for adapted Fitting–Marek–Truszczyński frames, strictly weaker than WF, with disjunction and finite-frame properties and modal companions.