Towards Designing Artificial Universes for Artificial Agents Under Interaction Closure

Abstract

We are interested in designing artificial universes for artificial agents. We view artificial agents as networks of highlevel processes on top of of a low-level detailed-description system. We require that the high-level processes have some intrinsic explanatory power and we introduce an extension of informational closure namely interaction closure to capture this. Then we derive a method to design artificial universes in the form of finite Markov chains which exhibit high-level processes that satisfy the property of interaction closure. We also investigate control or information transfer which we see as an building block for networks representing artificial agents. Introduction We are interested in designing artificial physics for artificial agents. This paper presents an exploratory step in this direction and also expounds the conceptual and the formal point of view we are taking. In this introduction we give a short overview of our approach and then proceed to formally define the different elements. Conceptually, we draw inspiration for our artificial physics and agents from “real” physics and living organisms. The artificial agents we have in mind are are minimally represented by networks of “high-level” or “macroscopic” processes. These high-level processes are derived from the underlying artificial physics. This situation is analogous to viewing living organisms as networks of processes (Maturana and Varela, 1980) on a mesoor macroscopic scale e.g. proteins or cells, and assuming an underlying physics e.g. elementary particle physics. Formally, we model our artificial physics simply as a univariate finite discrete time Markov process. We choose a univariate process because we do not want to presuppose any structure of the state space of the artificial physics. We also assume there is no downward causation (Campbell, 1974). This means that at all times, the high-level processes are causally dependent on the underlying physics. Loosely speaking, this means that the edges (interactions) of the high-level network of processes representing the agent are actually mediated by the low-level process. As we will see, this can formally be modelled using Bayesian networks. The final ingredient of our general approach tries to account for the success of doing science on scales larger than elementary particles e.g. atomic physics, chemistry and biology. To take this into account, we require that the highlevel processes are as predictive of other high-level processes as the underlying physics itself. In other words, the high-level processes at least appear to be directly causally related. Formally, we achive this by slightly extending the notion of informational closure introduced by Bertschinger et al. (2006) to two notions that we will call weak and strong interaction closure. Requiring informational closure already puts some constraints on the underlying process (Pfante et al., 2014) and so do interaction closures. Within this general setting we here inspect the situation where one high-level process seems to control another one. The idea is that any high-level network that represents an agent needs such a mechanism. Consider for example a sensor that writes its measurement to another process e.g. a memory for further processing. Another interpretation would be that the controlled process is part of the embodiment of the agent and therefore within the sphere of influence of the agent and shielded from the environment. The latter interpretation is related to the notion of embodiment put forward by Porr and Worgotter (2005). Yet another, more conservative, interpretation would be that the first process simply transfers information to the second. Information transfer is widely seen as an important part of decentralized computation (Lizier et al., 2014). Which in turn may be just what a network of processes representing an agent needs. Formally, we use an information theoretic notion, the transfer entropy (Schreiber, 2000), to quantify (here only apparent) control. Control and transfer entropy have been linked in another context by Touchette and Lloyd (2004). Note that the mechanism we treat is a requirement we introduce here in addition to interaction closure property. In order to arrive at a complete agent further mechanisms within larger networks are required. This will be investigated in future work. The results in this paper show that the requirements of strong interaction closure and control from a pair of highALIFE 14: Proceedings of the Fourteenth International Conference on the Synthesis and Simulation of Living Systems level processes put strong constraints on the dynamics of the underlying process. To arrive at these constraints we assume the ideal cases of both interaction closure and control. It should be seen as an advantage of the information theoretic measures we employ that they are both “soft”. This means they can readily be used to quantify also the degrees to which closure and control are present in a system.