Mathematical Theory of Intelligence (MIT)
About the school
The Mathematical Theory of Intellect (MIT) scientific school operates at the Faculty of Information Technologies of Taras Shevchenko National University of Kyiv. The head of the school is Professor Oleksiy Bychkov, Head of the Department of Software Systems and Technologies.
The subject of the school is the construction of intelligence as a formal mathematical object: with axiomatics, theorems, proofs and applications for solving problems of intellectual decision-making. This approach differs from the widespread “artificial intelligence” as an engineering simulation of cognitive abilities through neural networks. At mit, intelligence is treated as a subject of mathematical analysis, not as an engineering imitation.
Hereditary background -
Mit is the legal successor of the scientific school “Fuzzy Nonlinear Dynamics”, the founder of which is Professor O. S. Bychkov. In this previous school, the axiomatics of epistemic uncertainty was first proposed and developed into a complete description of nonlinear dynamical systems. The transition to a new name reflects the natural development of research: from the formalization of subjective perception of reality to the general formal theory of intelligence.
This transition is not a rejection of the previous work. The apparatus of hybrid automata of the school, the theory of functional stability, methods of (PN)-analysis for dynamics — all this continues to be the basis of MTI. The expansion of the topic occurred naturally: from the analysis of individual systems to the mathematical description of intelligence itself as the ability to make decisions under conditions of epistemic uncertainty.
Founder of the school
Bychkov Oleksii Serhiiovych — Laureate of the State Prize of Ukraine in the field of science and technology (closed topic, 2021), Academician of the Ukrainian Academy of Sciences, Doctor of Technical Sciences, Professor, Head of the Department of Software Systems and Technologies. Author of the modern theory of possibilities. Total experience of scientific work — 38 years, teaching — 23 years. He has been heading the department since 2014.
School Profile
The scientific school combines three interrelated areas of research that form a single methodological framework for the analysis, modeling and synthesis of complex intellectual systems.
1. Modern theory of possibilities
Development of the theory of possibilities as an alternative to the theory of probability and the theory of evidence of Dempster-Shafer to describe uncertainty in conditions of incomplete information. The school develops its own (PN)models, a formal apparatus of possible inference, metric characteristics of possible distributions, as well as an interpretation of the basic laws of quantum mechanics based on positive state coding and the theoretically possible Born postulate.
2. Nonlinear dynamics and hybrid automata
Investigation of the behavior of complex dynamic systems that combine continuous and discrete components. Development of a hybrid automaton apparatus for describing cyber-physical systems, software functional stability systems, as well as formal verification of the behavior of systems in dynamic environments. This is the direction of the doctoral dissertation of the founder of the school (2018, «Information technologies for the analysis and synthesis of continuous-discrete information systems»).
3. Artificial intelligence and intelligent autonomous systems
Creation of new architectures of intelligent systems at the intersection of neural networks, symbolic artificial intelligence and formal methods. Special emphasis is placed on multi-agent autonomous systems, cooperative coordination OF drone swarms, hybrid cognitive architectures (BDI + Behavior Trees + Neural Networks), and the application of capability theory to collective decision-making under uncertainty.
Current research projects
- Quantum mechanics without frequency interpretation: positive state coding and the theoretically possibility-oriented Born postulate (2025-present). Transfer of the modern theory of possibilities into a quantum-mechanical formal framework.
- Intelligent autonomous UAV swarm (2025-present) Creation of an intelligent autonomous swarm of UAVs with a three-level control architecture, hybrid cognitive agents, and fault tolerance mechanisms.
- The transferable training model (2025-present) Study of learning models that are transferred between different types and configurations of autonomous systems.
Partners & Collaboration
The school cooperates with Antonov State Enterprise, the National Academy of Medical Sciences of Ukraine (Institute of Traumatology and Orthopedics, Romodanov Institute of Neurosurgery), and the Ministry of Transport of Ukraine. It implements international academic mobility projects within the framework of Erasmus+ with universities in Bulgaria, the Czech Republic, Poland, Germany, as well as cooperation with the University of Le Mans (Le Mans Université, France).
Training of scientific personnel
Within the school, doctors of philosophy are trained in an educational and scientific program «Mathematical and software of automated and embedded systems». The list of topical topics of dissertation research has been expanded in the relevant section.
Relationship between directions
The three directions of the school do not exist in isolation. Possibility theory provides a formal apparatus for describing uncertainty in nonlinear dynamical systems and in intelligent agents. Nonlinear dynamics provides a mathematical foundation for modeling the behavior of these systems over time. Artificial intelligence provides tools for automatic learning and adaptation.The intersection of the three directions gives a unique methodology for creating intelligent autonomous systems with guarantees of correct behavior in conditions of incomplete information.