Axiomatic Theory of Rational Structures: A Formal Model of Reasoning

This work presents a formal theory of reasoning that models thought as an optimization process in a space of structures. The theory introduces four components of reasoning — I,T,C,O — and defines a metric on the space of structures, enabling quantitative comparison of reasoning strategies and explicit control over their properties. Based on this construction, the concept of contextual rationality is formulated, describing the quality of reasoning as a function of the task and its constraints. The proposed model addresses fundamental limitations of modern LLMs: the absence of a stable reasoning structure, the inability to control reasoning style, weak interpretability, and instability of conclusions. The theory provides a formal mechanism for selecting an optimal reasoning strategy, ensuring explainability, predictability, and adaptation of reasoning to context. The publication includes the preprint and presentation materials in both English and Russian. The work is intended for researchers in artificial intelligence, AI system architects, specialists in explainable AI, and anyone interested in the formalization of thought and the development of reasoning‑oriented models.