Recently I was self studying the properties of the Wronskian $W$ using various lecture notes and Wikipedia
I knew that if $W\ne0$ for at least one x then the functions are linearly independent
I also knew that by contrapositive, if the functions are linearly dependent then $W=0$ everywhere in the interval
Putting all the known facts about the Wronskian, I got the following diagram which illustrates all the logical statements that relates linear independence and the values of the Wronskian
Q1. Is this diagram a sort of generalization of a commutative diagram, as the arrows are not really a mapping from one set to another, but how one logical statement is related to another?
Q2. Is there any math discipline that explore a bunch of logical statements (or more generally, axioms and relations) as one giant mathematical structure, and/or geometrically, graphically?