Non decomposable connectives of linear logic

Abstract

This paper studies the so-called generalized multiplicative connectives of linear logic, focusing on the question of finding the “non-decomposable” ones, i.e., those that cannot be expressed as combinations of the default binary connectives of multiplicative linear logic, ⊗ (times) and ⅋ (par). In particular, we concentrate on generalized connectives of a surprisingly simple form, called “entangled connectives”, and prove a characterization theorem giving a criterion for identifying the undecomposable entangled ones.