| Abstract: | Extensions of Natural Deduction to Substructural Logics of IntuitionisticLogic are shown: Fragments of Intuitionistic Linear, Relevantand BCK Logic. Rules for implication, conjunction, disjunctionand falsum are defined, where conjunction and disjunction respectcontexts of assumptions. So, conjunction and disjunction areadditive in the terminology of linear logic. Explicit contractionand weakening rules are given. It is shown that conversionsand permutations can be adapted to all these rules, and thatweak normalisation and subformula property holds. The resultsgeneralise to quantification. |
