 In M this is equivalent to (P.4). Yet it is logically weaker, and it is easy to see that this suffices to block the entailment of (P.3) even in the presence of (P.1)–(P.2) (just consider a two-element model with mutual parthood, as in Figure 3, left). Still, (P.4c) is sufficiently stronger than (P.4a) and (P.4b) to rule out all three patterns in Figure 2, and it obviously preserves the spirit of (P.4)—if not the letter. The second sort of answer is to weaken Supplementation by adjusting the consequent. There are various ways of doing this, the most natural of which appears to be the following: