 Robert Kilwardby’s explanation is based on the view that convertible necessity premises are necessity propositions per se and not per accidens, like (8), which are not convertible. (See Notule libri Priorum 8.133–146.) In affirmative necessity propositions per se, the subject is per se connected to the predicate. In negative necessity propositions per se, the subject is per se incompatible with the predicate. The terms in per se inherences or incompatibilities are essential and necessarily stand for the things they signify. The historical background of Kilwardby’s interpretation is not clear; it does show similarities to Averroes’s discussion mentioned above, but there was no historical link. (See Lagerlund 2000, 25–42; Thom 2007, 19–28.)