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The aim of this paper is to present a mental AI-model based on a geometric representation of mental processes. This model can be considered as the first step in coming AI-formalization of foundations of psychoanalytic research.

1 Mathematical foundations for the present AI-model were developed in a series of works Khrennikov, 1997, 1998a,b, 1999a,b, 2000a,b, 2002a and Albeverio et al., 1999, and Dubischar et al, 1999. Unfortunately, the high level of mathematical presentation in these works makes them non readable for people working in AI, computer science, psychology. In the present article we would like to present the main distinguishing AI-features of our model without using the formal mathematical apparatus. Another important difference of this paper from mentioned works is that now we do not try to specify the set-theoretic and topological structure of mental space. In previous works we developed one special mathematical model of mental space given by hierarchical trees (so called utrametric spaces), see Khrennikov, 2004a, b, for neurophysiological basis for such spaces. Although such encoding of hierarchy into space topology is very promising (especially by taking into account the role of hierarchical structures in psychology), we find possible to proceed in modeling of flows of conscious/unconscious mind in the most general framework of arbitrary metric mental space. However, from the very beginning we emphasize that we could not exclude that practical creation of AI-psyche would be based on the hierarchical encoding of information by using trees equipped with ultrametric distance.

Our basic idea is to repeat in psychology and cognitive sciences the program of - - which has been performed in physics. And we hope that through such geometrization we shall be able to represent some elements of human psyche in the AI-framework. We recall that in physics the starting point of the mathematical formalization was creation of an adequate mathematical model of physical space. It was not so easy task. It took about three hundred years. However, finally, physicists got a well established model of space -- infinitely divisible real continuum. Physical systems where embedded in this space. Evolution of a physical system was represented by dynamical system (continuous—differential equation or discrete—itterations of some map from physical space into itself) . The basic dynamical law—the second Newton law—was given in a simple differential form. We would like to do the same with mind: a) to introduce mental space—"space of ideas" ; b) to consider dynamics in mental space—flows of ideas.

After performing such a nontrivial task, we apply our approach to modeling of Freud's psychoanalysis. Here we propose a mental AI-model describing flows of mind in the unconscious, the subconsciousness, and the consciousness as well as mental flows between these domains. The main attention will be paid to dynamics in the unconscious and the subconsciousness and their feedback coupling. Our model does not say so much about consciousness. Moreover, we are not sure that a mental AI-model could be applied to the problem of consciousness at all. Our model describes
(and can be even used for a mathematical simulation) of such basic features of psychoanalysis as repression of forbidden wishes, desires and impulses (coming to the subconsciousness from the unconscious and going to the consciousness), complexes and corresponding symptoms.

In a series of Models 1-4, we consider AI-modeling of cognitive systems with increasing complexity of psychological behavior determined by the structure of flows of ideas. One immediately recognizes that our models can be used for creation of AI-systems, which we call 	

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	, exhibiting important elements of human psyche. Creation of such psycho-robots may be useful improvement of - 	 	 At the moment domestic robots are merely simple working devices (e.g. vacuum cleaners or lawn mowers) . However, in future one can expect demand in systems which be able not only perform simple work tasks, but would have elements of human self-developing psyche.

2Such AI-psyche could play an important role both in relations between psycho-robots and their owners as well as between psycho-robots. Since the presence of a huge numbers of psycho-complexes (results of repression of forbidden desires) is an essential characteristic of human psychology, it would be interesting to model them in the AIframework.