Transitive Property or Law

This is a rule in mathematics and logic that says some properties can be transferred onto other things according to rules.

For example: I am a descendant of my father. My daughter is a descendant of me. Therefore, she is – by definition – a descendant of my father as well. The property of being a descendant transfers to my daughter because that’s how lineage works.

The classic example is from math. If a = b and b = c then logic dictates that a = c as well. The property of equality transfers from a to c through b.

Why I Looked It Up

I found it in a book, but I didn’t note the reference. I’ve also been vaguely aware of the concept for years.

I wrote this about hierarchical category in my second book:

With a category tree, you sometimes need to consider “implicit ancestral assignment”. If you have a tree of concepts – moving from broader to narrower as you traverse down the tree – does assignment in a child category imply assignment to all its parents as well?

Say your category tree has “Vehicles” with a child category of “Cars” which has a further child category of “Sedans.” If you assign something to “Sedans,” it should logically be assigned to “Cars” and “Vehicles” as well. Some APIs may support this, and others won’t.

Clearly, I’m talking about transitive inheritance there.