Checking for traits instead of types

In classic OOP, you often create superclasses and subclasses to group objects with similar capabilities. If you roughly model a group of felines in the animal kingdom with classes, you end up with a diagram that looks like this:

If you try to model more animals, you will find that it's a complex task because some animals share a whole bunch of traits, although they are quite far apart from each other in the class diagram.

One example would be that both cats and dogs are typically kept as pets. This means that they should optionally have an owner and maybe a home. But cats and dogs aren't the only animals kept as pets because fish, guinea pigs, rabbits, and even snakes are kept as pets. It would be tough to figure out a sensible way to restructure your class hierarchy in such a way that you don't have to redundantly add owners and homes to every pet in the hierarchy because it would be impossible to add these properties to the right classes selectively.

This...