Kolchinsky A, Wolpert DH. 2018 Semantic information, autonomous agency and non-equilibrium statistical physics. Interface Focus 8: 20180041. http://dx.doi.org/10.1098/rsfs.2018.0041
Abstract: Shannon information theory provides various measures of so-called syntactic information, which reflect the amount of statistical correlation between systems. By contrast, the concept of ‘semantic information’ refers to those correlations which carry significance or ‘meaning’ for a given system. Semantic information plays an important role in many fields, including biology, cognitive science and philosophy, and there has been a long-standing interest in formulating a broadly applicable and formal theory of semantic information. In this paper, we introduce such a theory. We define semantic information as the syntactic information that a physical system has about its environment which is causally necessary for the system to maintain its own existence. ‘Causal necessity’ is defined in terms of counter-factual interventions which scramble correlations between the system and its environment, while ‘maintaining existence’ is defined in terms of the system's ability to keep itself in a low entropy state. We also use recent results in non-equilibrium statistical physics to analyse semantic information from a thermodynamic point of view. Our framework is grounded in the intrinsic dynamics of a system coupled to an environment, and is applicable to any physical system, living or otherwise. It leads to formal definitions of several concepts that have been intuitively understood to be related to semantic information, including ‘value of information’, ‘semantic content’ and ‘agency’.From a special issue, ‘Computation by natural systems’ organised by Dominique Chu, Christian Ray and Mikhail Prokopenko .
The concept of semantic information refers to information which is in some sense meaningful for a system, rather than merely correlational. It plays an important role in many fields, including biology [1–9], cognitive science [10–14], artificial intelligence [15–17], information theory [18–21] and philosophy [22–24].1 Given the ubiquity of this concept, an important question is whether it can be defined in a formal and broadly applicable manner. Such a definition could be used to analyse and clarify issues concerning semantic information in a variety of fields, and possibly to uncover novel connections between those fields. A second, related question is whether one can construct a formal definition of semantic information that applies not only to living beings but also any physical system—whether a rock, a hurricane or a cell. A formal definition which can be applied to the full range of physical systems may provide novel insights into how living and non-living systems are related.
The main contribution of this paper is a definition of semantic information that positively answers both of these questions, following ideas publicly presented at the FQXi's 5th International Conference  and explored by Carlo Rovelli . In a nutshell, we define semantic information as ‘the information that a physical system has about its environment that is causally necessary for the system to maintain its own existence over time’. Our definition is grounded in the intrinsic dynamics of a system and its environment, and, as we will show, it formalizes existing intuitions while leveraging ideas from information theory and non-equilibrium statistical physics [33,34]. It also leads to a non-negative decomposition of information measures into ‘meaningful bits’ and ‘meaningless bits’, and provides a coherent quantitative framework for expressing a constellation of concepts related to ‘semantic information’, such as ‘value of information’, ‘semantic content’ and ‘agency’.