Evolution Theory of Self-Evolving Autonomous Problem Solving Systems

The present study is a continuation work of my previous work in the art:" Algebraic Net Class Rewriting Systems, Syntax and Semantics for Knowledge Representation and Aut omated Problem Solving" in Tirri SI (2013), and preliminaries as well as related notations are to be found there. Lots of studies have been driven to clarify routes between nodes e.g. in process algebra, important topics setting ground to game theories as well as overall in halting problems. On the other hand in more complex dimensional cases ordering definitions in sets of subgraphs have been under vigorous investigations mainly concentrated in tree structures. An amazingly minute portion of studies on gr aphs concentrates to relations between graphs and abstraction of them and one explanation for this might be that transformations on conceptual levels lead joints to a succinct model proper to syntax as well as to semantic domain requiring combining algebra ic structures to loop structured graphs and realizations of them, this requiring symbiosis of abstract syntax and real case sides. The most remarkable study of human abstraction mechanism yielding a concrete result especially within mathematics in the for m of analytical tools has been manifested by French philosopher, mathematician and physicist Ren é Descartes in the 17th century in his work " Regulae ad directionem ingenii, Règles utiles et claires pour la direction de l'Esprit en la recherche de la Vérité (1628)", freely outlining: "… a t first we must organize the things which are the most essential ones in conc entrating to do that by simplifying from phase to phase the vague, indefinite original pro b lem. Then we try to understand the relations between tho se simplified parts and then compare the propositions to be proved i.e. wise versa try to see the connections between the reached relations and the original problem.