Diference between Heraclit´s and Aristotel´s logic is that Arostotel defines not-A as oposite to A and Heraclit define not-A as diferent to A.If you came to the point in wich A and not-A are same you are not in position to think anymore.

Just oposite.If you want to talk in terms of diferent frameworks that leed you to modal logic ans semantic of possible worlds.There you will find definition of necessity and possibility.Something is necessary if exist in all possible worlds amd something is possible if can exist in some possible worlds.In short possibility is subset of necessity not vice versa.If you are interested in that Kripke is good source.