Abstract

Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and Plotkin's LF, with a representation mechanism: the language of RLF is the lL-calculus; the representation mechanism is judgements-as-types, developed for relevant logics. The lL-calculus type theory is a first-order dependent type theory with two kinds of dependent function spaces: a linear one and an intuitionistic one. We study a natural deduction presentation of the type theory and establish the required proof-theoretic meta-theory. The RLF framework is a conservative extension of LF. We show that RLF uniformly encodes (fragments of) intuitionistic linear logic, Curry's l I -calculus and ML with references. We describe the Curry-Howard-de Bruijn correspondence of the lL-calculus with a s...

Citations