Adaptive Agents and Complex Systems

In the definition given by G. Klir, a system S is defined as S = [M, R] where M is a set of objects and R is a set of relations between the objects. We can use this system definition to describe the Logic where the objects are propositions and the relations are the inferential rules. We can also describe the semantics of a linguistic text (semantic web) and many other disciplines. In spite of the success of the system model, we argue that a higher order of systems exists. The systems of order one are ordinary systems with objects and relations. The systems of order two are meta-systems where the relations are transformed into one another. Every transformation changes the relations which are in one context into the image of the same relations in another context. Transformations of relations or functions can be homomorphisms.