 A model for N\(_4\) consists in a set of world that is partitioned into normal and non-normal worlds. At every world, formulas are given one of four truth values, in accordance with Dunn’s semantics explained in section 2 above, with regard to conjunction, disjunction, and negation. But the treatment of implication is rather interesting. At normal worlds, an implication \(A\rightarrow B\), is true if and only if in every world w, if \(A\) is true in w, then \(B\) is also true in w. The implication is false if there is at least one world in which \(A\) is true and \(B\) is false. At non-normal worlds, implications are made true and false randomly. 