 More formally, a premise frame is a pair \(\langle W, \Gamma\rangle\) where \(W\) is a non-empty set of possible worlds and \(\Gamma: W \to \cP(\cP(W))\) is as a function assigning to any world \(w\) a set of propositions—the premises for \(w\). One may, but need not stipulate that \(w\) does, and all other worlds do not, belong to every proposition in \(\Gamma(w)\) (Centering). For the sake of simplicity, we assume that \(W\) is finite. A premise model is a triple \(M = \langle W, \Gamma, V\rangle\) such that \(\langle W, \Gamma\rangle\) is a premise frame and \(V\) a valuation function. For any proposition \(F\), let \(\Gamma(w)\bot F\) denote the set of all subsets of \(\Gamma(w)\) that are consistent with \(F\) but have no proper supersets in \(\Gamma(w)\) that are also consistent with \(F\). That is, \(\Gamma(w)\bot F\) is the set of subsets of \(\Gamma(w)\) that are maximally consistent with \(F\). The truth conditions for conditionals are: