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In referring to linear logic fragments, let M stand for multiplicatives, A for additives, 2 for second order quantifiers, and I for ïntuitionistic" version of linear logic fragments.
Lincoln, Scedrov, and Shankar showed the undecidability IMLL2 and IMALL2 (to appear in LICS '95). Lafont has subsequently proved the undecidability of MALL2 (to appear in the Journal of Symbolic Logic). It is the case that MLL2 is undecidable.
The paper is now available by anonymous ftp .
The paper is 8 pages long.