Cognitional Mechanics and Quantum Mechanics: Structural Isomorphism

Cognitional Mechanics (CM) establishes an axiomatic framework formalizing the structural mechanisms of intelligence. Unlike approaches based on physical dynamics or engineering, CM abstracts intelligence as a self-contained operational system defined by non-commutative operations, convergence of semantic states, and inaccessible domains (Zenodo DOI: https://zenodo.org/records/17993857). The framework positions intelligence as mathematically tractable, substrate-independent, and analyzable without external observation. CM reveals structural correspondences with Quantum Mechanics(QM), including operator non-commutativity, invariance of state vectors, and Planck’s constant analogously represented by the operational limit constant c. This demonstrates that intelligence mechanisms can be generalized and fully axiomatized. By defining a metric space of semantic states with distance functions satisfying non-negativity, symmetry, and the triangle inequality, CM ensures rigor and self-containment. The operational limit c serves as a logical boundary, absorbing measurability criticisms and ensuring convergence and inaccessibility are determined internally. CM provides a foundation for further study of intelligence’s geometric-operational structure, with implications for AI architectures, abstract metrics, and analogies to QM.