7.4 Intellectual Breadth: Quantifying the Generality of an Agent’s Intelligence 141
e the prior probability 0(6) according to some assumed distribution 0 e the effectiveness p(d, X) of 6 at predicting the actions of an agent X € ¥,
We may then define Definition 7 The inference ability of the agent 6, relative to and X, is Lyes, sim( X,Y )p(d,Y)
Dyes, sim(X, Y)
where sim is a specified decreasing function of d(X,Y), such as sim(X,Y) =
qu,x (8) = 8(8)
1 I+d(X,Y)°
To construct tx, we may then use the model of X created by the agent 6 € A with the highest inference ability relative to 4 and X (using some specified ordering, in case of a tie). Having constructed 7x, we can then say that
Definition 8 The inferred pragmatic general intelligence (relative to v and y) of a naturalistic agent X defined relative to an environment ys, is defined as the pragmatic general intelligence of the model rx of X produced by the agent 6 € A with maximal inference ability relative to js (and in the case of a tte, the first of these in the ordering defined over A). The inferred efficient pragmatic general intelligence of X relative to ys is defined similarly.
This provides a precise characterization of the pragmatic and efficient pragmatic intelligence of real-world systems, based on their observed behaviors. It’s a bit messy; but the real world tends to be like that.
7.4 Intellectual Breadth: Quantifying the Generality of an Agent’s Intelligence
We turn now to a related question: How can one quantify the degree of generality that an intelligent agent possesses? Above we have discussed the qualitative distinction between AGI and “Narrow AI”, and intelligence as we have formalized it above is specifically intended as a measure of general intelligence. But quantifying intelligence is different than quantifying generality versus narrowness.
To make the discussion simpler, we introduce the term “context” as a shorthand for “envi- ronment/interval triple (4,9,7).” Given a context (,9,7'), and a set »' of agents, one may construct a fuzzy set Agygr gathering those agents that are intelligent relative to the context; and given a set of contexts, one may also define a fuzzy set Con, gathering those contexts with respect to which a given agent 7 is intelligent. The relevant formulas are:
l Nu,9g,T(Q)V io TP XAgu er (®) = XCong (9.7) = 7 Dd, = Q 139 Q
where N = N(y,g,T) is a normalization factor defined appropriately, e.g. via N(y,9,T) = max Vi 9,7-
One could make similar definitions leaving out the computational cost factor Q, but we suspect that incorporating Q is a more promising direction. We then propose
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