 A state model is a tuple \({\langle S, \sqsubseteq, V \rangle}\) with \({\langle S, \sqsubseteq \rangle}\) a state space and \(V:\mathtt{P}\to (\wp(S) \times \wp(S))\) a valuation function returning not only set of states that make a given atom p true (abbreviated as \(V^+(p))\), but also the set of states that make it false (abbreviated as \(V^-(p))\). In principle, given an atom p, there needs to be no relation between the two sets. They might be overlapping \((V^+(p) \cap V^-(p) \neq \emptyset)\), thus yielding a state that makes p both true and false; they might be limited \((V^+(p) \cup V^-(p) \neq S)\), thus yielding a state that makes p neither true nor false; they might be neither, thus being exclusive \((V^+(p) \cap V^-(p) = \emptyset)\) and exhaustive \((V^+(p) \cup V^-(p) = S)\), and making the states behave as possible worlds with respect to p.