Relational Semantics for Distributive Linear Logic
Giancarlo Meloni, Luigi Santocanale · 2007
Axioms ruling linear negation have been investigated in the context of the complete semantics for distributive intuitionistic linear logic. Among these are the condition of being a dualizing element and the one of being a cyclic element. The motivation for analyzing other syntactic constraints comes from the observation that groupoids are models for classical linear logic. The analysis proceeds also in the opposite way: given semantic conditions, which could possibly hold in the canonical model of prime filters, equivalent syntactic conditions are found. Last, the relatioships among analyzed axioms are investigated, counterexamples are provided whenever there is no provability dependence. Keywords. Linear Logic, Quantales, Promonoidal Categories, Kripke Models, Distributive Lattices. Introduction. We have investigated axioms related to linear negation in the context of intuitionistic generalization of the complete semantics for Distributive Linear Logic presented in [GM]. We show (Sec...