On the Formalization of the Evolving Transformation System Model

The central concept of the Evolving Transformation System (ETS) model is struc-tural object representation constructed by the process of inductive inference. The model was proposed in 1990 by Lev Goldfarb to be applied to any pattern learning or classification problem. A formal exposition of the model is presented in this the-sis. It defines the concepts that encapsulate the idea of structural representation and includes lemmas and theorems that link these concepts together into a single model. The chosen form of definitions is related to several general postulates about structural representation. The main feature of this formalization of the ETS model is the presence of an infinite hierarchy of representational levels. At each level, object representations are constructed from primitive constructive transformations (building blocks). Primitive transformations of the next level correspond to complex context-dependent additive transformations of the previous one. This hierarchy allows to reduce the complexity of representation of an object by constructing its higher-level representation throug