 And stepping up again, industrial-strength paraconsistentists may hold that, though truth at the actual world is consistent, still entailment must preserve what holds in peculiar non-actual situations, some of which may be inconsistent (see Berto, 2007a, Ch. 5, and Priest, Beall and Armour-Garb, 2004, p. 6). The first three levels appear to be independent of dialetheism. (But for reason to worry that there is a ‘slippery slope’ from gentle to dialetheic paraconsistency, see Priest 2000. For particular worries about model theory, see Asmus 2012, and in the modal case, Martin 2015.) 