Abstract : The additive fragment of linear logic is complete for general (non-distributive) lattices. A sequent calculus for general lattices is presented with multiple antecedents and succedents. This construction is extended to give a sequent calculus for propositional linear logic with both additive and multiplicative contexts. Then, various decision procedures are investigated for general lattices.
Jean-Yves Marion. From multiple sequent for Additive Linear Logic to decision procedures for Free Lattices. Theoretical Computer Science, Elsevier, 1999, 224 (1-2), pp.157-172. ⟨inria-00098803⟩