One kind of generality in AI comprises methods for finding solutions that are independent of the problem domain. Allen Newell, Herbert Simon and their colleagues and students pioneered this approach and continue to pursue it.
Newell and Simon first proposed the General problem Solver GPS in their (1957) (also see (Ernst and Newell 1969). The initial idea was to represent problems of some general class as problems of transforming one expression into another by means of a set of allowed rules. It was even suggested in their (1960) that improving GPS could be thought of as a problem of this kind. In my opinion, GPS was unsuccessful as a general problem solver, because problems don't take this form in general and because most of the knowledge about the common sense needed for problem solving and achieving goals is not simply representable in the form of rules for transforming expressions. However, GPS was the first system to separate the problem solving structure of goals and subgoals from the particular domain.
If GPS had worked out to be really general, perhaps the Newell and Simon predictions about rapid success for AI would have been realized. Newell's current candidate for general problem representation is SOAR (Laird, Newell and Rosenbloom 1987), which, as I understand it, is concerned with transforming one state to another, where the states need not be represented by expressions.