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By exploring possible physical sense of notions, structures, and logic in aclass of noncommutative geometries, we try to unify the four fundamentalinteractions within an axiomatic quantum picture. We identify the objects andalgebraic operations which could properly encode the formation and structure ofsub-atomic particles, antimatter, annihilation, CP-symmetry violation, massendowment mechanism, three lepton-neutrino matchings, spin, helicity andchirality, electric charge and electromagnetism, as well as the weak and stronginteraction between particles, admissible transition mechanisms (e.g., muon tomuon neutrino, electron, and electron antineutrino), and decays (e.g., neutronto proton, electron, and electron antineutrino).

Towards an axiomatic model of fundamental interactions at Planck scale