Ay Nihat, Löhr Wolfgang
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany.
Faculty of Mathematics and Computer Science, University of Leipzig, PF 100920, 04009, Leipzig, Germany.
Theory Biosci. 2015 Dec;134(3-4):105-16. doi: 10.1007/s12064-015-0217-3.
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.
我们考虑一个与世界交互的智能体的感觉运动回路的通用模型。这将Uexküll的功能圈概念形式化。在此，我们假设一种特定的因果结构，用马尔可夫核进行机械描述。在这种一般性情况下，我们定义了世界中事件的两个σ代数，它们描述了两个各自的视角：（1）外部观察者的视角，（2）智能体的内在视角。从外部视角看，世界的并非所有方面都能被智能体所感知。这表现为第二个σ代数是第一个的子代数这一事实。我们提出较小的那个作为Uexküll的环境概念的形式化。我们表明，在连续性和紧致性假设下，世界的全局动态可以在不改变内部过程的情况下得到简化。这种简化可以作为系统为了与内部过程保持一致而必须具备的最小世界模型。
