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We explore the application of a new theory of Semantic Information to thewell-motivated problem of a resource foraging agent. Semantic information isdefined as the subset of correlations, measured via the transfer entropy,between agent $A$ and environment $E$ that is necessary for the agent tomaintain its viability $V$. Viability, in turn, is endogenously defined asopposed to the use of exogenous quantities like utility functions. In ourmodel, the forager's movements are determined by its ability to measure, via asensor, the presence of an individual unit of resource, while the viabilityfunction is its expected lifetime. Through counterfactual interventions --scrambling the correlations between agent and environment via noising thesensor -- we demonstrate the presence of a critical value of the noiseparameter, $\eta_c$, above which the forager's expected lifetime isdramatically reduced. On the other hand, for $\eta < \eta_c$ there islittle-to-no effect on its ability to survive. We refer to this boundary as thesemantic threshold, quantifying the subset of agent-environment correlationsthat the agent actually needs to maintain its desired state of staying alive.Each bit of information affects the agent's ability to persist both above andbelow the semantic threshold. Modeling the viability curve and its semanticthreshold via forager/environment parameters, we show how the correlations areinstantiated. Our work provides a useful model for studies of establishedagents in terms of semantic information. It also shows that such semanticthresholds may prove useful for understanding the role information plays inallowing systems to become autonomous agents.

Semantic Information in a model of Resource Gathering Agents