On Halldén Completeness of Modal Logics Determined by Homogeneous Kripke Frames
From Intuitionism to Brouwer's Modal Logic
We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this...
On interpolation in NEXT(KB.Alt(2))
We prove that there is infinitely many tabular modal logics extending KB.Alt(2) which have interpolation.
Interpolation in Normal Extensions of the Brouwer Logic
The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic.
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