Robotics, machine learning, inference, control, decision theory, system identification. There are many different views on how the information would flow from the environment into a robot, and the other way around. One example, Ralf Der is working on "homeokinesis". A robot is driven towards these regions in state space that cause large perceptual variations. To be able to do so, it necessarily must understand enough of the environment and hence won't just exhibit chaotic behavior.

Is there a branch of category theory that considers the fundamentals of a "self-learning" system? A description of a system which performs its own "system identification". It would be great if there is a formal approach to it, because many of the scientist working in this field (Oudeyer, Pfeiffer, Wolpert, Metta, Friston to name just a few) tend to explain their concepts in a narrative manner. It would be great to have a thorough conceptual review using monads, etc.

Challenges (from my laymen's perspective in increasing order of difficulty for a categorical approach):

Pointers to people who only tried(!) to apply category theory to these challenging problems will be also appreciated.

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    $\begingroup$ The word "sensorimotor" in the title, is a technical term or a typo? If it is a typo you might wish to edit it. $\endgroup$ – magma May 27 '13 at 8:18
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    $\begingroup$ It's the "default" term, see en.wikipedia.org/wiki/Sensorimotor with more than 2 million hits on Google. The alternative is "sensory-motor" which has fewer hits and looks ugly. $\endgroup$ – Anne van Rossum May 27 '13 at 9:26

Regarding "Describe Pearl's calculus of interventions" and other related ideas, you might find this thesis interesting:

  1. B. Fong, Causal Theories : A Categorical Perspective on Bayesian Networks, 2013.

Depending upon the level of speculation you are interested in considering, you might also like to look at this book:

  1. A. C. Ehresmann and J. P. Vanbremeersch, Memory Evolutive Systems; Hierarchy, Emergence, Cognition, Volume 4 (Studies in Multidisciplinarity). Elsevier Science, 2007, p. 402.
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  • $\begingroup$ Ah, I totally agree with the term "level of speculation" there. :-) I did like the little book I read from Rosen though, which apparently inspired Ehresmann and Vanbremeersch reading from one their paper's title "The Memory Evolutive Systems as a Model of Rosen’s Organisms – (Metabolic, Replication) Systems". I also found "Modeling Self-Organization With Nonwellfounded Set Theory" likewise inspired by Rosen. Especially thanks for the first link, nice! $\endgroup$ – Anne van Rossum May 26 '13 at 16:08

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