3rd TAGRA

This research explores a theoretical foundation for an intelligent machine capable of human-like reasoning through relational geometry, context, and self-reference. It proposes a framework for Quantum-Relational Artificial Intelligence based on Self-Referential Focal Relations (SRFR). The main idea is to represent information not simply as separate objects or states, but through the relationships between an observer and an object. The proposed information structure includes four elements: the relation between the subject and the object, the possibility of this relation, its necessity, and its temporal context. Inspired by Lotfi A. Zadeh’s possibility theory, possibility and necessity are used to describe incomplete knowledge without forcing it into a single probability value. In the proposed relational geometry, self-reference means that the relation itself becomes part of the information. The subject, the object, and their relation form one connected configuration. As a result, the system considers not only what is observed, but also how it is observed and from what relational position. The observer is therefore not an external label added to the information; the observer’s relation to the object is part of the information itself. The framework brings together Zadeh’s possibility theory, fuzzy relations, evidence-based reasoning, and ideas inspired by quantum information. It provides a way to describe an informational state through the object, the observer, their relation, and the surrounding context. This is a theoretical framework for further developing intelligent systems that can work with incomplete, uncertain, and changing knowledge. Future work will focus on developing rules for updating relational states, algorithms for interactions between SRFR nodes, and comparisons with probabilistic and neural approaches. The goal is to investigate whether relational geometry can provide a foundation for machines capable of more human-like forms of reasoning. This research is to connect human-like reasoning, relational geometry, ideas of quantum theory, and self-reference within one framework.