A Quantitative Theory of Cognition with Applications

Abstract

Cognition is based partly on belief and strives for knowledge of "truth". Description and the derived notion of control lead to notions of entropy and divergence and help to clarify what can be known, the "knowable", by setting limits to information. Via game theoretical considerations, a notion of core is introduced which, in classical settings, is related to that of exponential families. It facilitates the process of inference in concrete cases of interest. The basic setting is abstract. When we turn to probabilistic modelling, interaction between truth, belief and knowledge is essential for an interpretation of Tsallis entropy.