Relational proof system for linear and other substructural logics

In this paper we give relational semantics and an accompanying relational proof system for a variety of intuitionistic substructural logics, including (intuitionistic) linear logic with exponentials. Starting with the (Kripke-style) semantics for FL as discussed in [13], we developed, in [11], a relational semantics and a relational proof system for full Lambek calculus. Here, we take this as a base and extend the results to deal with the …