The denotational interpretation of a sequent calculus proof is, as usual, defined by induction.
In the meantime, sequent calculi provide a powerful organization of the knowledge specified through the formulae of the logic language taken into consideration.
Suppose now that in the sequent we have that and denote sets of occurrences of formulas.
The sequent can be seen as part of the verification condition which is generated during type-checking.
All the work cited above uses the formalism of linear sequent calculus.
In this section we present two formulations of linear logic: a one-sided sequent calculus and a two-sided sequent calculus.
In the present paper we define a sequent calculus associated to a linear functor in such a way that any linear functor provides a model.
Such a sequent is not an axiom unless a formula in that matches the facts in exists.
