  The main effect of admitting partially located properties into the system is that it is no longer the case that a property, P, and its complement, P′, are disjoint: they may now intersect. If the inferred property is partially located, then the class of “agreeing cases” (sapakṣas - places where the inferred property is present) and the class of “disagreeing cases” (vipakṣas—places where the inferred property is absent) overlap rather than being distinct classes. To put it another way, a property P should be thought of as having both a “presence range” (P+) and an “absence range” (P−), and the two may overlap. Consider now the standard inference “The mountain has fire, because it has smoke”. Suppose we find a place where smoke is present, and fire is both absent and also present, e.g. the kitchen. Does this show the inference to be faulty? According to definition V1, it does, because the kitchen will be a counter-example, a place where smoke is present and fire absent. But this is wrong: since fire is also present there, it is not a real counter-example to the rule “where there is smoke there is fire”. The upshot is that we must examine the “presence ranges” of the reason property and inferred properties, not their “absence ranges”. A real counter-example to rule is a case which is in the presence-range of the reason property but not in the presence range of the inferred property. 