The finite model property for various fragments of intuitionistic linear logic

Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for itituitionistic versions of those, i.e. intuitionistic MALL (which rye call IMALL). and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model properly for contractive li.rear logic (LLC). i.e. linear logic with contraction, and for its intuitionistic version (ILLC). The finite model property for related substructural logics also follow by our method. In particular, we shall show that the property holds for all of FL and GC(-) -systems except FLC and GL(C)(-) of One II II, that will settle the open problems stated in Ono [12].