On denotational completeness extended abstract

Jean-Yves Girard
1996 Electronical Notes in Theoretical Computer Science  
The founding idea of linear logic is the duality b e t ween A and A ? , w i t h v alues in ?. This idea is at work in the original denotational semantics of linear logic, coherent spaces, but also in the phase semantics of linear logic, where the A bilinear form B which induces the duality is nothing but the product in a monoid M, ? being an arbitrary subset B of M. The rather crude phase semantics has the advantage of being complete, and against all predictions, this kind of semantics had some
more » ... applications. Coherent semantics is not complete for an obvious reason, namely that the coherent space |interpreting ? is too small (one point), hence the duality between A and A ? expressed by the cut-rule cannot be informative enough. But
doi:10.1016/s1571-0661(05)80404-9 fatcat:j7wvc7xyarhxzogugvm5womkt4