Semantics

Linear Logic has numerous semantics some of which are described in details in the next sections.

• Coherent semantics
• Phase semantics
• Categorical semantics
• Relational semantics
• Finiteness semantics
• Geometry of interaction
• Game semantics

Common properties may be found in most of these models. We will denote by $A\longrightarrow B$ the fact that there is a canonical morphism from A to B and by $A\cong B$ the fact that there is a canonical isomorphism between A and B. By "canonical" we mean that these (iso)morphisms are natural transformations.