Logical and mathematical interpretation of decisions of intelligent agents

L.A. Lyutikova, M.S. Kochkarova

---

Abstract: Modern cybersecurity systems are faced with increasingly complex network architectures and a growing diversity of attack vectors. In this context, the ability of intelligent systems not only to effectively detect threats but also to rationalize their decisions is becoming increasingly important.
Аim. The work is to develop and experimentally verify a model of an RL agent capable of making decisions in a network environment, interpreted in terms of temporal and epistemic logic.
Results. This paper presents a formal approach to developing explainable reinforcement learning (XRL) for cybersecurity problems. This approach includes developing a mathematical model of an intelligent agent capable of detecting anomalies in network traffic and making decisions under uncertainty. A method for interpreting agent strategies is proposed, based on the use of linear temporal logic (LTL) and epistemic logic (EL), which ensures transparency, formal verifiability, and explainability of system behavior. It is demonstrated that the logical and mathematical interpretation of learned policies enables a transition from empirical dependencies to formalizable properties of security, liveness, and causality, thereby increasing the trust and reliability of cybersecurity systems. A computational experiment confirms the effectiveness of the proposed approach: anomaly detection accuracy reaches 94–96%, and the average response latency is less than 0.3 seconds.
Conclusion. The obtained results demonstrate the model’s high applicability for constructing explainable, verifiable, and resilient cybersecurity systems, and also demonstrate that logical interpretation of strategies contributes to increased decision transparency and strengthens trust in intelligent information security systems. The experiment demonstrate that the agent is capable of achieving high threat detection accuracy with short response times, and the resulting logical formulas successfully pass specification feasibility checks. This confirms that logical interpretation of strategies increases the transparency and trust in the decisions of intelligent systems.

Keywords: model, interpretation, logical analysis, reinforcement learning, agent, explainable artificial intelligence

For citation. Lyutikova L.A., Kochkarova M.S. Logical and mathematical interpretation of decisions of intelligent agents. News of the Kabardino-Balkarian Scientific Center of RAS. 2025. Vol. 27. No. 6. Pp. 125–134. DOI: 10.35330/1991-6639-2025-27-6-125-134

References

1. Sutton R.S., Barto A.G. Reinforcement learning: an introduction. 2nd ed. MIT Press, 2020.
2. Rybakov V.V. Intransitive linear temporal logic, knowledge from past, decidability, admissible rules. arXiv preprint arXiv: 1503.08761. 2015.
3. Doshi-Velez F., Kim B. Towards a rigorous science of interpretable machine learning. arXiv preprint arXiv:1702.08608, 2017.
4. Rudin C. Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence. 2019. Vol. 1. Pp. 206–215.
5. Wang Ya., Yu W., Seligman J. Quantifier-free epistemic term-modal logic with assignment operator. Annals of Pure and Applied Logic. 2022. Vol. 173. No. 3. P. 103071. DOI: 10.1016/j.apal.2021.103071
6. Nguyen T.T., Reddi V.J. Deep reinforcement learning for cyber security. Computers & Security, 2022. Vol. 113. P. 102583. DOI: 10.1109/TNNLS.2021.3121870
7. Baier C., Katoen J.-P. Principles of Model Checking. MIT Press, 2008.
8. Shoham Y., Leyton-Brown K. Multiagent systems: algorithmic, game-theoretic, and logical foundations. Cambridge University Press, 2009.
9. Bashmakov S.I., Kosheleva A.V., Rybakov V.V. Unification in temporal multi-agent logics with universal modality. Mathematics in the Modern World: Abstracts of the International Conference (August 14–19, 2017). Novosibirsk: IM SO RAS, 2017. P. 67. (In Russian)
10. Wolter F.M., Zakharyaschev M. Undecidability of the unification and admissibility problems for modal and description logics. ACM Transactions on Computational Logic. 2008.
    Vol. 9. No. 4. P. 25.
11. Lyutikova L.A. Methods for improving the efficiency of neural network decision-making. Advances in Automation IV. RusAutoCon 2022. Lecture Notes in Electrical Engineering. 2023. Vol. 986. Pp. 294–303. DOI: 10.1007/978-3-031-22311-2_29

Information about the authors

Larisa A. Lyutikova, Leading Researcher, Department of Neuroinformatics and Machine Learning, Institute of Applied Mathematics and Automation – branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
89 A, Shortanov street, Nalchik, 360000, Russia;
lylarisa@yandex.ru, ORCID: https://orcid.org/0000-0003-4941-7854, SPIN-code: 1679-7460
Madina S. Kochkarova, Assistant, Department of Digital Engineering and Network Technologies, North Caucasian State Academy;
36, Stavropolskaya street, Cherkessk, 369001, Russia;
madina_kochkarova_94@mail.ru