Quantum systems with diagonal singularity: Their logic and intrinsic irreversibility

The work of the Brussels-Austin group on irreversibility over the last years has shown that quantum large Poincaré systems with diagonal singularity lead to an extension of quantum theory beyond the conventional Hilbert space framework and logic. We characterize the algebra of observables, and the states and the logic of the extended quantum theory of intrinsically irreversible systems with diagonal singularity.