10.3 Steps Toward A (Formal) General Theory of General Intelligence 179 10.3 Steps Toward A (Formal) General Theory of General Intelligence Now begins the formalism. At this stage of development of the theory proposed in this chapter, mathematics is used mainly as a device to ensure clarity of expression. However, once the theory is further developed, it may possibly become useful for purposes of calculation as well. Suppose one has any system S (which could be an AI system, or a human, or an environment that a human or AI is interacting with, or the combination of an environment and a human or Al’s body, etc.). One may then construct an uncertain transition graph associated with that system 5, in the following way: e The nodes of the graph represent fuzzy sets of states of system S' (I'll call these state-sets from here on, leaving the fuzziness implicit) e The (directed) links of the graph represent probabilistically weighted transitions between state-sets Specifically, the weight of the link from B to A should be defined as P(o(S, A, t(T))|o(S, B, T)) where o(S, A, T) denotes the presence of the system S in the state-set A during time-distribution 7, and f¢() is a temporal succession function defined so that ¢(7') refers to a time-distribution conceived as "after" T. A time-distribution is a probability distribution over time-points. The interaction of fuzziness and probability here is fairly straightforward and may be handled in the manner of PLN, as outlined in subsequent chapters. Note that the definition of link weights is dependent on the specific implementation of the temporal succession function, which includes an implicit time-scale. Suppose one has a transition graph corresponding to an environment; then a goal relative to that environment may be defined as a particular node in the transition graph. The goals of a particular system acting in that environment may then be conceived as one or more nodes in the transition graph. The system’s situation