  Indexed Linear Logic has been introduced by Ehrhard and Bucciarelli, it can
be seen as a logical presentation of non-idempotent intersection types extended
through the relational semantics to the full linear logic. We introduce an
idempotent variant of Indexed Linear Logic. We give a fine-grained
reformulation of the syntax by exposing implicit parameters and by unifying
several operations on formulae via the notion of base change. Idempotency is
achieved by means of an appropriate subtyping relation. We carry on an in-depth
study of indLL as a logic, showing how it determines a refinement of classical
linear logic and establishing a terminating cut-elimination procedure.
Cut-elimination is proved to be confluent up to an appropriate congruence
induced by the subtyping relation.
