The Mathematical Abstraction Theory, The Fundamentals for Knowledge Representation and Self-Evolving Autonomous Problem Solving Systems

Abstract

The study represents a new way to describe knowledge with generalized universal algebra allowing loop structures so very important in AI languages and which gives an extensive variety of notional relations between net entities without restricting the semantic use. Consequently a new syntax model for solving problems defined by said nets is established flexibly utilizing notional similarities with original problems to further match solutions in memory data banks thus additionally creating transducer graphs of solving rewrite systems and thereof closure system of solving classes. The study introduces universal partitioning to widen environmental attachments subject to abstraction relations, yielding universal macros from parallel TD-solutions. Net NUO-presentations are delivered providing more general coverage enabling net block homomorphism to be used for TD-solution generation. A special attention is given to cardinalities of basic solutions. Second order parallel relation is introduced for distinct solution set bases. Finally direct products of power sets in abstraction relations serve as ingredients for multiple level abstraction algebra which is taken in account for determining self-evolving solving systems. This is reached by tree different stages offering combinational approach in multiple power solution families and iterative solving, thus creating solution basis for evolutional levels.