Denotational Semantics for Polarized (But-non-constrainted) LK by Means of the Additives

Following the idea that a classical proof is a superimposition of ‘constructive’ proofs, we use the linear connective “&” to define an embedding Pa of polarized but non-constrained LK in linear logic, which induces a denotational semantics. A classical cut-elimination step is now a cut-elimination step in one of the ‘constructive slices’ superimposed by the classical proof.