 Semantic structures for counterfactual conditionals involving impossible worlds were first introduced by Routley 1989, and have been proposed e.g. by Read 1995, Mares &amp; Fuhrmann 1995, Mares 1997, Nolan 1997, Brogaard &amp; Salerno 2013, Bjerring 2014, Berto et al. 2018. Most of these are natural extensions of Lewis’s 1973 semantics for counterfactuals and capture several intuitions about counterpossible reasoning. The main task for such theories consists in accounting for the concepts of closeness and qualitative similarity between worlds once impossible worlds enter the stage. How to fine-tune these notions is not a trivial matter (for an extensive discussion, see Vander Laan 2004; we will say more in  section 4.2).