Non-commutative logic II: sequent calculus and phase semantics

Non-commutative logic, which is an uniication of commutative linear logic and cyclic linear logic, is extended to all linear connectives: additives, exponentials and constants. We give two equivalent versions of the sequent calculus | directly with the structure of series-parallel order varieties, and with their presentations as partial orders |, phase semantics and a cut elimination theorem.