Conditional statements and inter-type relationships.
Most people who have studied fields that relate to the usage of formal logic know the three statements that can be derived from a conditional (if-then) statement. For those of you not in school anymore, here's a recap:
Given an if-then statement "if p then q", where p is the hypothesis and q is the conclusion...
The converse is the exchange of the hypothesis and conclusion of the original statement, therefore "if q then p";
The inverse is the negation of the hypothesis and conclusion of the original statement, therefore "if not p then not q";
The contrapositive is the inverse of the converse of the original statement, therefore "if not q then not p".
I was up thinking last night, as I am prone to doing, and thought of a connection between quasi-identical relations and dual relations. These are oversimplifications of the relations themselves, but you could define quasi-identity as initial similarity leading to long-term dissimilarity, and you could define duality as initial dissimilarity leading to long-term similarity. I know that they're not exactly conditional statements, but you could say given the system above that duality is the converse of quasi-identity, and vice versa.
What are your thoughts, if any, on this? Have you experienced duality to be converse to quasi-identity? What relations could be inverse or contrapositive to each other? Have I finally gone crazy?