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The Umwelt of an embodied agent - a measure-theoretic definition
Publikationstyp
Journal Article
Date Issued
2015-12-09
Sprache
English
Author(s)
Journal
Volume
134
Issue
3/4
Start Page
105
End Page
116
Citation
Theory in Biosciences 134 (3/4): 105-116 (2015-12)
Publisher DOI
Scopus ID
PubMed ID
26650201
Publisher
Springer
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 (Formula presented.) -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 external perspective, are accessible to the agent. This is expressed by the fact that the second (Formula presented.) is a subalgebra of the first one. We propose the smaller one as formalisation of Uexküll’s Umwelt concept. We show that, under continuity and compactness assumptions, the global dynamics of the world can be simplified without changing the internal process. This simplification can serve as a minimal world model that the system must have in order to be consistent with the internal process.
Subjects
Embodied agent
External observer
Function-circle
Intrinsic perspective
Sensorimotor loop
Umwelt
σ-Algebra
DDC Class
570: Biowissenschaften, Biologie