Decidability of linear affine logic

Abstract

The propositional linear logic is known to be undecidable. In the current paper we prove that the full propositional linear affine logic containing all the multiplicatives, additives, exponentials, and constants is decidable. The proof is based on a reduction of linear affine logic to sequents of specific "normal forms" and on a generalization of Kanovich computational interpretation of linear logic adapted to these normal forms. © 2001 Academic Press.