Authors: Lutz Strassburger ; Anupam Das ; Ryuta Arisaka

We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the standard modal logics K4, S4, and S5. We use for our presentation the formalism of nested sequents and give a syntactic proof of cut elimination.

Comment: 33 pages

• 03B20 - Subsystems of classical logic (including intuitionistic logic)
• 03B45 - Modal logic (including the logic of norms)
• 03F05 - Cut-elimination and normal-form theorems