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Information theory provides a nice way to quantify this, but it's not the only possible avenue
A proper mathematical theory of abstraction should provide formal ways to quantify generalization.
something in the lines of Galois connection?
I ping @MonniauxD on that topic, he knows abstraction better than me I'm sure
Cf Kurt Gödel.
What do you have in mind?
Category Theory is known as abstract general nonsense 
One approach might be: 1 - formulate AI system as a mapping 2 - select method to quantify degree of mapping invariance accross spaces 3 - define set of spaces which span set of “general” problems we care about 4 - compute ave degree of mapping invariance across those spaces
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