Abstract
In studies of machine perception and learning, and in the simulation of the adaptive control aspects of human behaviour one of the basic problems is that of obtaining suitable representations of the environment. The signal sources in the external world are essentially continuous in time and space, while their internal representations are generally discontinuous, being both sampled and quantized. The relationship, for example, between the continuous world of physics and the perceived world of discrete objects is not a simple one psychologically and an investigation of this relationship is important both to human and artificial intelligence theory. In this paper certain basic invariance requirements on the trajectories of a dynamical system in a quantized state space are analysed to obtain relationships between the dynamical and logical properties of the system, and a method for generating internal representations is presented.
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