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Item type:Publication, Access status: without files , The Umwelt of an embodied agent - a measure-theoretic definitionWe 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.Publicationtype: Journal ArticleScopus© Citations 16 17 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Process dimension of classical and non-commutative processesWe treat observable operator models (OOM) and their non-commutative generalisation, which we call NC-OOMs. A natural characteristic of a stochastic process in the context of classical OOM theory is the process dimension. We investigate its properties within the more general formulation, which allows to consider process dimension as a measure of complexity of non-commutative processes: We prove lower semi-continuity, and derive an ergodic decomposition formula. Further, we obtain results on the close relationship between the canonical OOM and the concept of causal states which underlies the definition of statistical complexity. In particular, the topological statistical complexity, i.e. the logarithm of the number of causal states, turns out to be an upper bound to the logarithm of process dimension.Publicationtype: Journal Article23