Models for Substructural Arithmetics

Abstract

This paper explores models for arithmetic in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find negation complete models for arithmetic in R.