Invariants and Symmetries among Adaptive Agents

Abstract

In this paper we present agents and systems at different order of complexity. At the first order we have agents which acts are transformations from one state to another. At the second order the actions of the agents transform one context with rules and data to another context with other rules and data. In the transformation of the second order the new rules and the new data are projected in the new context. Rules of the new context must be adapted to the new rules obtained by the transformation. The adaptation process can be obtained by a close loop control inside the possible set of the rules included in the new context. Close loop control at the second order can be obtained by the second order action of the agents. Invariants and symmetry are possible when we move from one context to another. A set of contexts can be transformed in another set of contexts by a third order action of a meta-agent. In conclusion a hierarchical tower of agents and meta agents can be built in a way to generate complex transformations.