Poly-contextural Modeling of Heterarchies in Brain Functions

All Hebbian rules which are discussed in the literature of neuromorphic nets are embedded within the principle of ultrametricity corresponding directly to hierarchical structures. In order to describe and to model simultaneously distributed parallel neural activities as they occur in heterarchically organized systems (self-referentiality) which cannot be linearized, a formal system for an adequate description of structural circularities and ambiguities is necessary. A basis for such a formal system is given by the theory of poly-contexturality, in which multi-negational operators regulate the duality principles of complementarity, and transjunctional operators produce multi-simultaneous heterarchical structures. 1 I N T R O D U C T I O N One of the criticisms most often heard about Artifcial Intelligence (AI) is that machines cannot be called intelligent until they are able to learn to do new things and to adapt to new situations, rather than simply doing as they were told to do. There can be little question that adaptibility to new surroundings and to solve new problems is an important characteristics of intelligent entities. Rather than discussing in advance whether it is possible for computers to "learn", it is more enlightening to try to describe what activities we mean when we say "learning" and what algorithms are necessary to model those activities. One of the very general standard definitions of learning is "a change in performance (for the better, as a function of experience)", a definition which is rather black-box-like and uninformative for the design of any technical device being able to learn. In the following discussion we will restrict ourselves to a cybernetical description of learning processes as it was discussed, for example, by Bateson (Bateson, 1972) using Russell's theory of (logical) types as descriptive basis for a classification of different learning processes. Despite of its usefulness and success in various scientific disciplines, Bateson's model is strongly hampered by the use of the theory of logical types especially if the design of technical entities is envisaged. The shortcomings of this learning model have been discussed elsewhere (von Goldammer & Kaehr, 1989) and will not be repeated here. The significance of Bateson's studies is founded methodologically by their logical analysis and description of communication processes such as 'learning'. Keeping the phenomenological part of his classification, we will distinguish between three categories of 'learning':