I'll need help with this question, as I am not sure I understand what is being asked, as we covered a lot of things. With regards to polyatomic ions, if they are oxyanions (a negative ion with one or more oxygens attached attached to a nonmetal, the ones that end with -ate tend to have more oxygens than the ones that end with -ite. And with the exception of nitrogen, the common oxyanions have the same charge as the monatomic anion.
But I would not consider these "rules" in a "rules based logic system" for nomenclature, but a good "rule of thumb" that works for the set of chemicals we are dealing with in this class.
Hope that helps