200 11 Stages of Cognitive Development
Implication
My eye is facing a block and it is not dark
A relationship is created describing the block’s color Similarity
My body
My teacher’s body
|- Implication
My teacher’s eye is facing a block and it is not dark A relationship is created describing the block’s color
This sort of inference is the essence of Piagetan “theory of mind.” Note that in both of these implications the created relationship is represented as a variable rather than a specific relationship. The cognitive leap is that in the latter case the relationship actually exists in the teacher’s implicitly hypothesized mind, rather than in CogPrime’s mind. No explicit hypothesis or model of the teacher’s mind need be created in order to form this implication-the hypothesis is created implicitly via inferential abstraction. Yet, a collection of implications of this nature may be used via an uncertain reasoning system like PLN to create theories and simulations suitable to guide complex inferences about other minds.
From the perspective of developmental stages, the key point here is that in a CogPrime context this sort of inference is too complex to be viably carried out via simple inference heuristics. This particular example must be done via forward chaining, since the big leap is to actually think of forming the implication that concludes inference. But there are simply too many combinations of relationships involving CogPrime’s eye, body, and so forth for the PLN component to viably explore all of them via standard forward-chaining heuristics. Experience- guided heuristics are needed, such as the heuristic that if physical objects A and B are generally physically and functionally similar, and there is a relationship involving some part of A and some physical object R, it may be useful to look for similar relationships involving an analogous part of B and objects similar to R. This kind of heuristic may be learned by experience—and the masterful deployment of such heuristics to guide inference is what we hypothesize to characterize the concrete stage of development. The “concreteness” comes from the fact that inference control is guided by analogies to prior similar situations.
11.4.3 The Formal Stage
In the formal stage, as shown in Figure 11.7, an agent should be able to carry out arbitrarily complex inferences (constrained only by computational resources, rather than by fundamental restrictions on logical language or form) via including inference control as an explicit subject of abstract learning. Abstraction and inference about both the sensorimotor surround (world) and about abstract ideals themselves (including the final stages of indirect learning about inference itself) are fully developed.
Formal stage evaluation tasks are centered entirely around abstraction and higher-order inference tasks such as:
1. Mathematics and other formalizations.
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