  We introduce a non-associative and non-commutative version of propositional
intuitionistic linear logic, called propositional non-associative
non-commutative intuitionistic linear logic (NACILL for short). We prove that
NACILL and any of its extensions by the rules of exchange and/or contraction
are undecidable. Furthermore, we introduce two types of classical versions of
NACILL, i.e., an involutive version of NACILL and a cyclic and involutive
version of NACILL. We show that both of these logics are also undecidable.
