Final Report Summary - LOGICIC (The Logical Structure of Correlated Information Change) In this project we have designed a unified logical framework for representing and analyzing various forms of correlated information change. We analyzed a wide range of very different information-gathering phenomena which do have one specific feature in common, namely the very act of learning new information may directly change the reality that is being learnt. On the one hand we have focused on the way in which an introspective agent changes her beliefs when learning new higher-order information, i.e. information that may refer to her own beliefs. On the other hand we have analyzed situations in which an observer learns about a phenomenon by performing observations that may perturb the very phenomenon under study, as in the case of quantum measurements or observations in the social sciences. With this variety of case studies ranging over classical and quantum phenomena, the research team has worked on the design of a logical framework which can be used to analyze and compare these phenomena. The key ingredient of this unifying framework is “logical dynamics”, and in particular the dynamic-epistemic notions of conditional which play a central role to understand the mentioned forms of correlated information change. When zooming in more specifically, a probabilistic dynamic quantum logic is used to analyze quantum actions, including quantum measurements and entanglement. To analyze specific scenarios in which the more complex forms of correlated belief change can be observed, involving phenomena known in the Social Sciences such as "pluralistic ignorance" and "informational cascades", techniques from dynamic epistemic logic are adopted. With respect to the latter line of work, the results of this project show that the designed logical models of “Informational Cascades” can provide support for the counter intuitive claim that informational cascades can be the direct consequence of individual “rationality”. Hence contrary to what one would expect, when giving agents unbounded higher-order reasoning powers (i.e. an unrestricted capacity to reason about all higher-levels of belief and allowing them to conclude that they are part of a cascade) may still not be enough for them to break a rational cascade. While such cascades are not likely to occur, our result shows that if they do then they may be unavoidable by “rational” means. In another line of work, this project focuses on belief revision that is directed towards the truth, i.e. on “learning”. One of the main results obtained in this context refers to the logical analysis of the cognitive difficulty of children who are learning deductive reasoning steps. In collaboration between the LogiCIC project and researchers in Psychology at the University of Amsterdam, a proof-theoretic method is used to perform a task analysis of logical reasoning steps. The measures that are derived from this analysis give a good prediction of the empirical findings based on results obtained for the deductive version of a Mastermind game (implemented within the Dutch on-line educational learning platform called "Math Garden"). In a related context, team members have been exploring scenarios of "group learning". Here the focus is directed towards groups of agents who can learn from each other via a process of public communication and deliberation. The central idea of this investigation is to focus on the factors that may interrupt or prevent groups to realize their full epistemic potential. In this interdisciplinary project, we combine insights and techniques from a range of research domains, including logic, quantum mechanics, philosophy of science, belief revision theory, truth approximation and learning theory. For more information about the seminars and workshops that have been organized in the context of this project, we refer to the project’s website:https://sites.google.com/site/logicicproject/home
