 In 1980, Nicholas Rescher and Robert Brandom published The Logic of Inconsistency. A Study in Non-Standard Possible-Worlds Semantics and Ontology. They introduced a modal semantics including, besides ordinary possible worlds (taken as maximally consistent collections of states of affairs), also non-standard worlds that are locally inconsistent (such that, for some \(A\), both \(A\) and \(\neg A\) hold at them), and incomplete (such that for some \(A\), neither \(A\) nor \(\neg A\) hold at them).  These are obtained combinatorially, via two recursive operations having standard worlds as their base, and called schematization \((\cap)\) and superposition \((\cup)\).  Given two worlds \(w_1\) and \(w_2\), a schematic world \(w_1 \cap w_2\) is one at which all and only the states of affairs obtain, which obtain both at \(w_1\) and at \(w_2\). Dually, a “superposed” or inconsistent world \(w_1 \cup w_2\) is one at which all and only the states of affairs obtain, which obtain at \(w_1\) or at \(w_2\). Rescher and Brandom’s inconsistent-superposed worlds are, therefore, impossible worlds of the fourth kind: Contradiction Realizers making both \(A\) and its negation true, for some \(A\) (just superpose, for instance, a possible world, \(w_1\), at which I am 1.70m tall, and another possible world, \(w_2\), at which I am 1.90m tall).