Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
74/2015

The 'Umwelt' of an Embodied Agent - A Measure-Theoretic Definition

Nihat Ay and Wolfgang Löhr

Abstract

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 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 external perspective, are accessible to the agent. This is expressed by the fact that the second σ-algebra 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.

Received:
Oct 28, 2015
Published:
Oct 29, 2015
Keywords:
Umwelt, function-circle, sensorimotor loop, embodied agent, intrinsic perspective, external observer, σ-algebra

Related publications

inJournal
2015 Repository Open Access
Nihat Ay and Wolfgang Löhr

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

In: Theory in biosciences, 134 (2015) 3-4, pp. 105-116