Non-Commutativity, Incompatibility, Emergent Behavior and Decision Support Systems
M. Canan · Procedia Computer Science · 2018
The whole is greater than the sum of its parts (WGSP) is one of the principles that attempt to explain an emergent behavior in complex systems. A conceptual WGSP approach can provide rational explanations. Whereas, a probabilistic study may demonstrate deviations from rational WGSP predictions. For example, conjunction-disjunction fallacies, and information order effects in inference are among the issues that classical probability theory (CPT) fails to explain. CPT is based on set theory rules which require that the probability of a single event is always greater or equal to the probability of joint events that are challenged by empirical findings. Developments in cognitive science introduced the application of quantum probability theory (QPT) to the problems of macro-systems. QPT provides coherent-dynamic explanations and a unified framework to study the deviations from the CPT predictions. This paper discusses how can QPT offer a coherent mathematical answer to the WGSP and improve the understanding of the emergent behavior in cyber-physical systems. Secondly, a Google search data is discussed in which order of the available information entails a non-commutative search result. Since the order of information matters, a Bayesian model may fail to recognize noncommutative probabilistic outcomes. QPT can predict the order effects for Google search situations.