*4.1. Figure I*

In the proofs of the strongly valid syllogisms in Theorems 8, 10, 11 and 12, we use monotonicity to weaken the conclusion. In these Theorems, we can see that we can order strongly valid syllogisms by monotonicity into triangles.

In Theorem 15, we order, by monotonicity, the strongly valid syllogisms into columns. In Theorem 15, we proved the syllogisms by strengthening the first premise.
