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

Publikationstyp

Journal Article

Publikationsdatum

2015-12-09

Sprache

English

Author

Enthalten in

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.