Three Topics in Non-decomposability of Generalized Multiplicative Connectives

Abstract

Danos and Regnier introduced generalized (non-binary) multiplicative connectives in Danos and Regnier [2]. They showed that there exist generalized multiplicative connectives that cannot be defined by any combination of the tensor and par rules in the multiplicative fragment of linear logic. Such connectives are called non-decomposable generalized multiplicative connectives [2, p.192]. The non-decomposability of logical connectives can be regarded as a proof-theoretic and syntactic counterpart of functional completeness for cut-free proofs. In this short note, we investigate Danos and Regnier's notion of non-decomposability and present three results concerning the (non-)decomposability of generalized multiplicative connectives.