Operational Ontology of Cognition:Integrating OST, TMDD, and MM as a Foundation for Explainable, Inductive, and Synthetic AI

Modern AI architectures, including foundation models and multi-agent systems, have reached the limits of the approximation paradigm. They efficiently interpolate within the training distribution but still operate on correlations without an explicit ontology of objects, causes, and states. This limits their ability for induction (generation of new concepts), causal reasoning, and cross-domain knowledge synthesis. This work proposes an Operational Ontology of Cognition based on three complementary formal approaches: Operational Set Theory (OST) as a model of the cognitive act of distinction, Tensor Model of Discrete Dynamics (TMDD) as the physics of complex systems, and Mazein Mechanics (MM) as dynamics with double constraint. Intelligence is interpreted not as statistical approximation of a function, but as a process of ontological coordination, governed by the triad of transformers: Inertia (I), Generator (G), and Dissipator (D). Within the proposed architecture, learning is formalized as restructuring of a feature system P(t), existence is defined by reaching a threshold w(x) ≥ θ, knowledge synthesis is represented as a structural intersection A⋏B of ontologies, and induction is defined as the minimization of structural restructuring ∆(M(t), M(t+1)). Such an AI does not require abandoning the existing foundation model infrastructure: an ontological control layer is introduced on top of it, transforming large language and multimodal models from statistical mirrors into sensory and linguistic organs of a cognitive system possessing its own operational ontology.