Decision problems for second-order linear logic

The decision problem is studied for fragments of second order linear logic without modalities. It is shown that the structural rules of contraction and weakening may be simulated by second order propositional quantifiers and the multiplicative connectives. Among the consequences are the undecidability of the intuitionistic second order fragment of propositional multiplicative linear logic and the undecidability of multiplicative linear logic with first order and second order quantifiers.