Toolkit for VASSes

There are many natural problems for VASS systems, which are a bit similar in style to the reachability problem, but cannot be directly reduced to reachability.
In order to solve them one needs to dig into involved solutions to the reachability problem and modify the proof.
I will present a few axioms (formalizing some aspect of the reachability-likeness) such that every problem fulfilling these axioms is decidable for VASS languages.