Logical-mathematical interpretation of strategies of intelligent agents in soil condition monitoring tasks

The article proposes a formal approach to explainable reinforcement learning focused on monitoring soil conditions under the influence of natural factors and anthropogenic impacts. It examines a digital twin of the soil profile in sloped areas where, after the application of fertilizers, non-stationary processes are observed: moisture infiltration, nutrient leaching, over-saturation, changes in acidity, and surface runoff. These processes possess stochastic nature and significant spatial-temporal variability, complicating the application of traditional deterministic or threshold methods. A model of an intelligent agent has been developed, which assesses the dynamics of key soil parameters (moisture at different depths, concentrations of nitrates and phosphates, pH, electrical conductivity, surface runoff coefficient) and makes decisions about the adjustment of agronomic interventions. The proposed approach integrates field monitoring data, physical laws of soil-hydrological processes, and reinforcement learning methods, enabling the agent to adapt to changing environmental conditions and predict the development of anomalous states. To ensure interpretability and formal verifiability of the agent's behavior, the use of temporal logic (LTL) and epistemic logic (EL) is suggested. These formalisms allow for transitioning from empirically derived strategies to strict verifiable properties, describing the correctness of responses to over-saturation and leaching, the attainability of the target agrochemical state, the sequence of actions after rain events, as well as the dependency of the agent's decisions on the information available to it under partial observability of the soil profile. The logical interpretation enables the extraction of understandable agronomic rules of the "if-then" type, consistent with the physics of the processes and soil management practices. A computational experiment was conducted using data obtained from an experimental site, including time series of observations on rainfall events, infiltration, filtration, and slope movements of moisture. The trained agent demonstrated high accuracy in detecting soil anomalies (93-96%), resilience to noise in the data, and low response latency.