Specific and complete local integration of patterns in Bayesian networks

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We present a first formal analysis of specific and complete local integration. Complete local integration was previously proposed as a criterion for detecting entities or wholes in distributed dynamical systems. Such entities in turn were conceived to form the basis of a theory of emergence of agents within dynamical systems. Here, we give a more thorough account of the underlying formal measures. The main contribution is the disintegration theorem which reveals a special role of completely locally integrated patterns (what we call ι-entities) within the trajectories they occur in. Apart from proving this theorem we introduce the disintegration hierarchy and its refinement-free version as a way to structure the patterns in a trajectory. Furthermore we construct the least upper bound and provide a candidate for the greatest lower bound of specific local integration. Finally, we calculate the ι-entities in small example systems as a first sanity check and find that ι-entities largely fulfil simple expectations.
Original languageEnglish
Article number230
Number of pages46
Issue number5
Publication statusPublished - 18 May 2017


  • identity over time
  • Bayesian networks
  • multi-information
  • entity
  • persistence
  • integration
  • emergence
  • naturalising agency


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