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.
"A completeness theorem for symmetric product phase spaces." J. Symbolic Logic 69 (2) 340 - 370, June 2004. https://doi.org/10.2178/jsl/1082418530