 System B, proposed by Burgess, is the smallest extension of CK containing ID, OR and CMon. System B axiomatizes the truth conditions stated under (VSC)-o assuming \(\preceq\) is a preorder (reflexive and transitive). Another specific interest of system B is that its flat fragment corresponds to the system P of nonmonotonic logic due to Kraus, Lehmann and Magidor (see  section 3.4).  System P is also sound and complete for Adams’ probabilistic semantics of conditionals (see  section 5),  and a three-valued characterization can be given for it too, as mentioned above, see Dubois and Prade (1994). In that sense, system P is quite central amongst logic of conditionals.