[My apologies for writing this as an answer, despite the fact that it is basically just a comment to the previous answer. But I am not allowed to post a comment up there, since I do not have enough "reputation"]
The previous answer is not correct. Linear logic (as well as any of its substructural systems: MLL, MALL, MELL, ALL, whatever you want...) is perfectly monotone.
Neel's answer confuses "relevance" and "non-monotonicity".
Relevance can be seen as non-monotonicity of the inference connector of the system. Linear logic is relevant, in that the provability of $\;\vdash A \multimap B$ does not imply the provability of $\vdash X\otimes A \multimap B$. Relevance is a sort of inner non-monotonicity of the logic.
On the other side, what people call non-monotonic logics are systems where the provability itself of the system is not monotone: adding a new element to the set of formulas changes the set of provable formulas. It is a form of meta non-monotonicity, because it concerns provability and not the connector of inference. Linear logic is monotone: you can add whatever you want to the set of formulas, and any new axiom or inference rule to the system, but if you had a proof of the sequent $\;\Gamma \vdash M: A$ before, you will still have it now, for you have not changed the other inference rules of the sequent calculus.
As far as I know, (real) non-monotonic logics are hard to put down in a sequent calculus form enjoying cut-elimination, or any other type of proof system with an equivalent notion of terminating proof-reduction. This is why the tradition categorical semantic approaches hardly would work for them.