  Danos and Regnier introduced generalized (non-binary) multiplicative
connectives in (Danes and Regnier, 1989). They showed that there exist the
generalized multiplicative connectives which cannot be defined by any
combinations of the tensor and par rules in the multiplicative fragment of
linear logic. These connectives are called non-decomposable generalized
multiplicative connectives (ibid, p.192). Non-decomposability of logical
connecives can be considered as a proof-theoretical and syntactical counterpart
of the functional-completeness on cut-free proofs. In this short note, we
investigate the notion of Danes and Regnier's non-decomposability and give
three results concerning (non-)decomposability of generalized multiplicative
connectives.
