142 7 A Formal Model of Intelligent Agents
Definition 9 The intellectual breadth of an agent 7, relative to the distribution v over environments and the distribution y over goals, is
H(XGonq (Hs 951)
where H is the entropy and
V(L)V(G, HK) XConx (Hg, L)
S2 (ta) 1(98; Ho) XCon, (Has 981 Tw) (He GB -T.)
XConn (u, g; T) =
is the probability distribution formed by normalizing the fuzzy set xcon, (1, 9,T).
A similar definition of the intellectual breadth of a context (y, 9,7), relative to the distri- bution o over agents, may be posited. A weakness of these definitions is that they don’t try to account for dependencies between agents or contexts; perhaps more refined formulations may be developed that account explicitly for these dependencies.
Note that the intellectual breadth of an agent as defined here is largely independent of the (efficient or not) pragmatic general intelligence of that agent. One could have a rather (efficiently or not) pragmatically generally intelligent system with little breadth: this would be a system very good at solving a fair number of hard problems, yet wholly incompetent on a larger number of hard problems. On the other hand, one could also have a terribly (efficiently or not) pragmatically generally stupid system with great intellectual breadth: i.e a system roughly equally dumb in all contexts!
Thus, one can characterize an intelligent agent as “narrow” with respect to distribution v over environments and the distribution + over goals, based on evaluating it as having low intellectual breadth. A “narrow AI” relative to v and y would then be an AI agent with a relatively high efficient pragmatic general intelligence but a relatively low intellectual breadth.
7.5 Conclusion
Our main goal in this chapter has been to push the formal understanding of intelligence in a more pragmatic direction. Much more work remains to be done, e.g. in specifying the environment, goal and efficiency distributions relevant to real-world systems, but we believe that the ideas presented here constitute nontrivial progress.
If the line of research suggested in this chapter succeeds, then eventually, one will be able to do AGI research as follows: Specify an AGI architecture formally, and then use the mathematics of general intelligence to derive interesting results about the environments, goals and hardware platforms relative to which the AGI architecture will display significant pragmatic or efficient pragmatic general intelligence, and intellectual breadth. The remaining chapters in this section present further ideas regarding how to work toward this goal. For the time being, such a mode of AGI research remains mainly for the future, but we have still found the formalism given in these chapters useful for formulating and clarifying various aspects of the CogPrime design as will be presented in later chapters.
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