The logical content of the axioms of these theories is expressed by the geometry of sequent calculus rules, which have only atomic formulas as active and principal.
Cut elimination permits structural proof analysis, and syntactic proofs of conservativity results.
The Journal of Symbolic Logic, vol. Admissibility of structural rules in contraction-free systems for intuitionistic logic, manuscript, 1997. Bounds for cut elimination in intuitionistic propositional logic, Archive for Mathematical Logic, vol. S. Negri, J. von Plato. Cut elimination in the presence of axioms, manuscript, 1998.