STRUCTURAL ONTOLOGY Formal Foundations of a Theory of the Domains of Reality

This work presents Structural Ontology, a theory developed to investigate the structural conditions necessary for the existence of an objective, intelligible, and structurally coherent reality. Starting from a set of primitive definitions, axioms, and theorems, it develops an ontological architecture introducing the concepts of Ontological Domains, Structural Identity, Ontological Transitions, and Ontological Foundation, while establishing the formal relations among these elements. The theory is subsequently synthesized through a formal signature, defined as SO = (C, Φ), and complemented by derived structures intended for the mathematical development of its components. Structural Ontology is not proposed as a particular description of reality, nor as a theory competing with existing scientific, philosophical, or theological models. Rather, its purpose is to provide a common formal language capable of representing, comparing, and investigating different ontological models according to the same structural principles. Within this framework, the Ontological Foundation is not introduced as a philosophical or religious presupposition, but is deduced as a consequence of the theory's own axiomatic architecture. The present document therefore establishes the conceptual, deductive, and formal foundations of a research program devoted to the development of models, derived structures, and applications of Structural Ontology in philosophy, logic, mathematics, cosmology, and philosophical theology.