In a previous work with Antonio Bucciarelli, we introduced
indexed linear logic as a tool for studying and enlarging the
denotational semantics of linear logic. In particular, we showed how
to define new denotational models of linear logic using
symmetric product phase models (truth-value models) of
indexed linear logic. We present here a strict extension of indexed
linear logic for which symmetric product phase spaces provide a
complete semantics. We study the connection between this new system
and indexed linear logic.