Structural Interactions and Absorption of Structural Rules in BI Sequent Calculus

Development of a contraction-free BI sequent calculus, be it in the sense of G3i or G4i, has not been successful in literature. We address the open problem by presenting such a sequent system. In fact our calculus involves no structural rules

On Nested Sequents for Constructive Modal Logics

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 page

Structural Interactions and Absorption of Structural Rules in BI Sequent Calculus

Development of a contraction-free BI sequent calculus, be the contraction-freeness implicit or explicit, has not been successful in the literature. We address this problem by presenting such a sequent system. Our calculus involves no structural rules. It should be an insight into non-formula contraction absorption in other non-classical logics. Contraction absorption in sequent calculus is associated to simpler cut elimination and to efficient proof searches