Hi FG,
Thanks for the question! The easiest way to see how and why this works is to use a numerical example. In A <--m-- B --m--> C, let's imagine there are 5 Bs. If 3 of them are As, and 3 of them are Cs, then there's no way to avoid an overlap of A and C, hence the inference A
C.
In something like A
B
C, there is a way to avoid overlap. Let's say there are 3 As, 9 Bs, and 100 Cs. If 2 of the As are Bs, then most As are Bs. But if 5 of Bs are Cs, then those 5 Bs that are Cs don't have to include the 2 As. So, it could be that none of the As are C, or that some of them are, or even that all of them are. We simply don't know enough to draw a solid inference about the relationship of A and C.
In the case where A
B, and C
B (that is, both arrows point at B), the problem is that B could be a larger group and thus there doesn't have to be an overlap. For example, let's say there are 3 As, 1000 Bs, and 3 Cs. The 2 As and 2 Cs that are Bs don't have to overlap, and hence we cannot conclude that A
C.
The one time you can get an inference out of A
B
C is when each group is of roughly similar size, or that the group sizes get progressively smaller (there' more to it than just the group sizes diminishing in size, but that's the gist). For example, let's say there were 5 As, 5 Bs, and 5 Cs. In that case, you know that at least one of the As is a C, which allows for the inference that A
C.
Please let me know if that helps. Thanks!
