 Earlier we mentioned that system P corresponds to the flat fragment of system B. Given the centrality of system P, here we say more about the way Kraus, Lehmann and Magidor defined it as a system of nonmonotonic logic. KLM do not aim at characterizing which formulae are logically valid, but at specifying closure conditions for rational sets of conditionals. They read the conditional \(A&gt;C\) (actually they use the notation \(A\pipsim C\)), with \(A\) and \(B\) only from \(L_0\), as expressing a default of the form “if \(A\) then normally \(C\)” or “\(C\) is a plausible consequence of \(A\)”. They start with models right away, but their models are slightly different from the ones we have seen so far. Importantly, KLM have no use for a truth value of a conditional at a single world, but only look at the “consequence relation” determined by a full model. What KLM call “states” are more like information states than like possible worlds, what they call “worlds” are valuations, i.e., assignments of truth values to the propositional variables of the language. KLM’s preferential models are similar to the o-models discussed above, except there is only one binary relation for the full model rather than one for each world in the model.