CAS may be viewed as systems composed of interacting agents which behaviour is described in terms of rules. Each of these agents that form part of the system has its own behaviour that adapt by changing their rules as experience accumulates. The problem is that considering this adaptability in each part of the system, the CAS’s behaviour abound in nonlinearities. This problem is at the same time the beauty of the system because from this, the system reach the adaptation, and “adaptation is the sine qua non of CAS” (1)
Due the interconnectivity between all the agents that compose the CAS, each of them exerts an influence over the others. It has as consequence that all change in the behaviour of one of the agents affect the behaviour of the total system. Considering that the agents are in constant change because the continuum process of learning-adapting, then the CAS shows a temporal adaptation that is coherent with the change of all of its parts.
Among the CAS’s examples that exist in the nature is important o mention the economic, ecological and social systems. The social problems, and the ecological ones are considered to be complex because their emergency. Both of them have been studied from a complex system perspective introducing methods of statistical physics and has been considered like CAS (2).
(1) Holland, J.H. “Hidden Order How Adaptation Builds Complexity” 1996 Perseus Books Cambridge Massachusetts.
(2) Pascual, M., and Dunne, J.A. 2006 “From Small to Large Ecological Networks in a Dynamic World.” In Ecological Networks Linking Structure to Dynamics in Food Webs, ed. by M. Pascual, J.A. Dunne Santa Fe Institute Studies in the Sciences of Complexity 3-24 Oxford University Press.
Margarita Mayoral-Villa 
The apparent “non-linearity” seen biologically-based multi-agent complex adaptive systems shares the seeming “unpredictability” of quantum mechanics. It is becoming more obvious that “bio-logic” is quantum logic, and so the “complexity” seen in biologically-based multi-agent complex adaptive systems (e.g. eukaryotic organisms, corporations, or governments) is in reality a quantum logic phenomenon. Deutsch said that a system of quantum logic in a quantum computer must utilize quantum mechanics as a resource, and the links below are to abstracts of two related papers that deal with such theoretical considerations.
http://proceedings.aip.org/resource/2/apcpcs/1316/1/287_1?isAuthorized=no
http://spiedigitallibrary.org/proceedings/resource/2/psisdg/8057/1/80570P_1?isAuthorized=no
Thanks a lot for your comments and the references. I agree with you about the “unpredictability” of quantum mechanics. However I am not so sure that could be applied this point of view at CAS. I will read the abstracts, may be it could help me to have a better understanding of the CAS emergency.
It is the definition of emergent concepts that they are outside of the realm of what can be logically deduced from what is known at the level of their components. This is in essence the idea of Godel’s incompleteness theorems.
The following is a quote from an article entitled “TRUTH IN COMPLEX ADAPTIVE SYSTEMS MODELS SHOULD BE BASED ON PROOF BY CONSTRUCTIVE VERIFICATION” by David Shipworth (Worldviews, Science And Us: pp. 141-155).
“‘Emergent’ properties of complex adaptive systems (CAS) models create particular epistemological and ontological challenges. These challenges bear directly on current debates in the philosophy of mathematics and in theoretical computer science. CAS research, with its emphasis on computer simulation, is heavily reliant on models which explore the entailments of Formal Axiomatic Systems (FAS). The incompleteness results of Gödel, the incomputability results of Turing, and the Algorithmic Information Theory results of Chaitin, undermine a realist (platonic) truth model of emergent properties.”