 But this is not a valid deduction, since if A is assumed to be true and B false, the conclusion that follows, not-A, remains false despite both premises being true.  If, on the other hand, Boethius means his reader not to take them for sentences but rather, following Aristotle’s syllogistic, terms, which carry no truth-value by themselves, then the inference schema can be given a valid interpretation, as long as one allows for the way that Boethius understood negation and compound conditionals (see Martin 2009, 76–78). If a thing is A then it must be that if it is B then it is C. So, if we also have that if it is B then it is not-C, then it could not be A, so it must be not-A.  This example alone thus already suggests that, despite some formal similarities to sentential logic, Boethius is actually operating with something more akin to the term logic that preceded him rather than in some newer, original, pre-modern formulation of sentential logic. 