A Relevant Analysis of Natural DeductionS

We study a framework, RLF, for deening natural deduction presentations of linear and other relevant logics. RLF consists in a language together, in a manner similar to that of LF, with a representation mechanism. The language of RLF, the-calculus, is a system of rst-order linear dependent function types which uses a function to describe the degree of sharing of variables between functions and their arguments. The representation mechanism is judgements-as-types, developed for linear and other relevant logics. The-calculus is a conservative extension of the-calculus and RLF is a conservative extension of LF.