> So now I wonder if your concerns are addressed [...]
My concerns haven't got past the mapping of propositions to things which can be added and multiplied.
If we call the map f, and if propositions means all propositions built up from some atomic propositions, then it is reasonable to ask what f(not-p), f(p OR q), f(p AND q) and f(p => q) map to, and how (such things as) de Morgan's laws come into the picture.
Also, I am still unsure what those 'things which can be added and multiplied' are.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting