 To illustrate the extra power (4.2) gives us (over (4.1) and (NP)), consider Simplification, the inference from \(A \wedge B\) to \(A\), or Disjunction Introduction, from \(A\) to \(A \vee B\). (4.2) directly entails that there are worlds where these rules fail. So, if we find (4.2) plausible, we can infer that impossible worlds are not, in general, governed by standard  paraconsistent logics.  A paraconsistent logic is any one in which cont radictory premises \(A\), \(\neg A\) do not entail arbitrary conclusions. But standardly, paraconsistent logics maintain the principle that conjunctions are true just in case both conjuncts are; disjunctions are true just in case at least one disjunct is; and double negations \(\neg \neg A\) are true just in case \(A\) is. If we accept (4.2), then these relationships will break down in some impossible worlds.