PHP Cascading Object Inheritance Defaults

I’m still new to some aspects of object oriented programming.  I’ve been stuck on this one problem for quite a bit now.  I’d like to build a hierarchy of objects, where the child object inherit’s it’s parents and grandparents default property.

It seemed like such a simple thing to do, but the more I messed with it, the more it boggled my mind.  I was trying to extend a base classes and merge the defaults while i add more information to every extended class.   Take for example the following code:

I wanted class C to have the defaults of all parent classes. The above code works and outputs:

Array ( [a] => A [b] => B [c] => C )

Thanks to Stephan Miller for helping me figure this out.