By A.I. Mal'cev
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5. The material realm corresponds to the environment. The biological level includes the sensors and the eﬀectors while the cognitive level corresponds to the cycle including “mark” and “eﬀect” organs. 3 Circular Schema Circular reactions have been emphasized in the study of action schema done by Piaget (Piaget 1970, 1971). Piaget called his general theoretical framework ”genetic epistemology” because he was primarily interested in how knowledge develops in living organisms. Cognitive structures are patterns of physical or mental actions that underlie speciﬁc acts of intelligence and correspond to the stages of development.
This has the advantage that it is a conﬁguration that is shareable across diﬀerent domains. The self-similarity allows parallel processing with similar software. 3 Modelling Statistical Information The categorical and multi-layered structure starts to be practically used in statistical data processing implementations (McCullagh 2002). The relational database introduced in the statistical information systems is a signiﬁcant tool used to store statistical data and to design the data structure of a speciﬁc statistical data processing application, as an IRDS.
Sk =. . =s. Let D denotes the common transition matrix of the component processes. The transition matrix C∗D with “∗” a tensor product describes the whole process at the conditioning level m=1. It is a stochastic matrix too. The resulting processes have been studied as conditional stochastic processes. The tensor product “∗” connects diﬀerent conditioning levels. The same method of construction, via the tensor product “∗”, may be continued for a number of conditioning levels. Interesting PSMs arise if K and S-processes are tensors and are deﬁned on diﬀerent types of algebraic frames, that is, for diﬀerent categories.