I have put on my web page a link toward a "pdf" slide giving the main "map of the territory". http://iridia.ulb.ac.be/~marchal/MapOfTerritory.pdf It is a graph whose vertex give the main propositional logics used in the "derivation of physics from machine introspection", and the edges are just inclusion relations. For exemple CL = propositional classical logic, as seen as the set of all theorems of some (complete) presentation of it. Or as the set of all classical tautologies. IL = Intuitionistic logic; and QL = quantum logic. (Precise definitions will be given) Both IL and QL are sublogic of CL. (A v (not A)) is not a theorem of IL, for example, and A & (B v C) and (A & B) v (A & C) are not equivalent in QL. Above CL we find the main modal logic: the "well known" G and G*, and S4Grz, etc.
That little diagram should help. Print and sleep with it ;-) More explanation asap.