Abstract

In this paper, we introduce connectification operators for intuitionistic and classical linear algebras corresponding to linear logic and to some of its extensions withn-contraction. In particular,n-contraction (n2) is a version of the contraction rule, wheren+1 occurrences of a formula may be contracted ton occurrences. Since cut cannot be eliminated from the systems withn-contraction considered most of the standard proof-theoretic techniques to investigate meta-properties of those systems are useless. However, by means of connectification we establish the disjunction property for both intuitionistic and classical affine linear logics withn-contraction.