Text extracted via OCR from the original document. May contain errors from the scanning process.
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 in the environment at any point in time may also
be associated with one or more nodes in the transition graph; then, the system’s movement
toward goal-achievement may be associated with paths through the environment’s transition
graph leading from its current state to goal states.
It may be useful for some purposes to filter the uncertain transition graph into a crisp
transition graph by placing a threshold on the link weights, and removing links with weights
below the threshold.
The next concept to introduce is the world-mind transfer function, which maps world (envi-
ronment) state-sets into organism (e.g. AI system) state-sets in a specific way. Given a world
state-set W, the world-mind transfer function MZ maps W into various organism state-sets with
various probabilities, so that we may say: M(W) is the probability distribution of state-sets the
organism tends to be in, when its environment is in state-set W. (Recall also that state-sets are
fuzzy.)
Now one may look at the spaces of world-paths and mind-paths. A world-path is a path
through the world’s transition graph, and a mind-path is a path through the organism’s transi-
HOUSE_OVERSIGHT_013095