The Umwelt of an embodied agent—a measure-theoretic definition

@article{Ay2015TheUO,
  title={The Umwelt of an embodied agent—a measure-theoretic definition},
  author={Nihat Ay and Wolfgang L{\"o}hr},
  journal={Theory in Biosciences},
  year={2015},
  volume={134},
  pages={105-116}
}
  • N. Ay, Wolfgang Löhr
  • Published 9 December 2015
  • Computer Science, Medicine, Mathematics, Physics
  • Theory in Biosciences
We consider a general model of the sensorimotor loop of an agent interacting with the world. This formalises Uexküll’s notion of a function-circle. Here, we assume a particular causal structure, mechanistically described in terms of Markov kernels. In this generality, we define two $$\sigma $$σ-algebras of events in the world that describe two respective perspectives: (1) the perspective of an external observer, (2) the intrinsic perspective of the agent. Not all aspects of the world, seen from… 
The Bayesian stance: Equations for ‘as-if’ sensorimotor agency
  • S. McGregor
  • Psychology, Computer Science
    Adapt. Behav.
  • 2017
TLDR
The approach is straightforward: Pearl’s causal formalism is used to identify physical variables at the causal boundary between ‘agent’ and ‘environment’, and identify these with variables in Bayesian decision theory; this provides a rigorous bridge between mathematical models of physics and mathematical model of rational decision-making.
Information , Control , and Learning – The Ingredients of Intelligent Behavior September 26-28 , 2016
Nihat Ay – Max Planck Institute for Mathematics in the Science Mathematical Aspects of Embodied Intelligence I will present recent results on the design of embodied systems with concise control
On Invention of Structure in the World: Interfaces and Conscious Agents
  • C. Prakash
  • Computer Science
    Foundations of Science
  • 2019
TLDR
Two theorems showing that a conscious agent can consistently see geometric and probabilistic structures of space that are not necessarily in the world per se but are properties of the conscious agent itself are discussed, suggesting the need for a new theory which resolves the reverse mind-body problem.
Interpreting Dynamical Systems as Bayesian Reasoners
TLDR
This work focuses on the case in which a system can be interpreted as performing either Bayesian filtering or Bayesian inference, and provides formal definitions of what it means for such an interpretation to exist, using techniques from category theory.
Expanding the Active Inference Landscape: More Intrinsic Motivations in the Perception-Action Loop
TLDR
This article reconstructs the active inference approach, locate the original formulation within, and show how alternative intrinsic motivations can be used while keeping many of the original features intact, and illustrates the connection to universal reinforcement learning by means of the formalism.
How Morphological Computation Shapes Integrated Information in Embodied Agents
TLDR
This article combines different methods in order to examine the information flows among and within the body, the brain and the environment of an agent to calculate the optimal policy for goal-directed behavior based on the “planning as inference” method.
Morphological Computation: Synergy of Body and Brain
TLDR
This paper argues for a synergistic perspective, and studies a new measure of synergistic information and discusses an algorithm that allows the calculation of the measure in non-trivial (non-binary) systems.
The Computational Boundary of a “Self”: Developmental Bioelectricity Drives Multicellularity and Scale-Free Cognition
  • M. Levin
  • Psychology, Medicine
    Front. Psychol.
  • 2019
TLDR
A fundamental definition of an Individual based on the ability to pursue goals at an appropriate level of scale and organization is proposed and a formalism for defining and comparing the cognitive capacities of highly diverse types of agents is suggested.
A Theory of Morphological Intelligence
TLDR
The question of quantifying morphological intelligence from observational data is examined, given a time series of a recorded behaviour, to post hoc determine how much of the behaviour was controlled by the brain and how much resulted from the exploitation of the body-environment dynamics.
Unknotting reciprocal causation between organism and environment
In recent years, biologists and philosophers of science have argued that evolutionary theory should incorporate more seriously the idea of ‘reciprocal causation.’ This notion refers to feedback loops
...
1
2
...

References

SHOWING 1-10 OF 27 REFERENCES
Information Theory of Decisions and Actions
TLDR
Using a graphical model, a recursive Bellman optimality equation for information measures is derived, in analogy to reinforcement learning; from this, new algorithms for calculating the optimal trade-off between the value-to-go and the required information- to-go are obtained, unifying the ideas behind the Bellman and the Blahut–Arimoto iterations.
Higher Coordination With Less Control—A Result of Information Maximization in the Sensorimotor Loop
This work presents a novel learning method in the context of embodied artificial intelligence and self-organization, which has as few assumptions and restrictions as possible about the world and the
Comparison between Different Methods of Level Identification
TLDR
This study is restricted to the case of discrete dynamical systems, where the different levels are linked by a coarse-graining of variables and states of the system.
Operator-theoretic identification of closed sub-systems of dynamical systems
TLDR
This paper presents a systematic method of identifying those closed sub-systems of a given discrete time dynamical system in the frame of operator theory and it is shown that this problem is closely related to finding invariant sigma algebras of the dynamics.
On the Causal Structure of the Sensorimotor Loop
In recent years, the application of information theory to the field of embodied intelligence has turned out to be extremely fruitful. Here, several measures of information flow through the
Measure Theory
These are some brief notes on measure theory, concentrating on Lebesgue measure on Rn. Some missing topics I would have liked to have included had time permitted are: the change of variable formula
Probability Theory
TLDR
This course will want to find conditions that allow us to compute expectations by taking limits, i.e., to force an equality in Equation (1) to force the Monotone Convergence Theorem.
Umwelt und Innenwelt der Tiere
THIS is one of the most interesting summaries of biological work that has appeared recently. Written by one who has had a large share in physiological research, it deals in an intimate manner with
Theoretical Biology
THE publisher of the International Library of Psychology, Philosophy, and Scientific Method are to be congratulated not only on the inclusion in their collection of this peculiarly interesting
Causality: Models, Reasoning and Inference
1. Introduction to probabilities, graphs, and causal models 2. A theory of inferred causation 3. Causal diagrams and the identification of causal effects 4. Actions, plans, and direct effects 5.
...
1
2
3
...