The work of the Brussels-Austin groups on irreversibility over the last years has shown that Quantum Large Poincaré systems with diagonal singularity lead to an extension of the conventional formulation of dynamics at the level of mixtures which is manifestly time asymmetric. States with diagonal singularity acquire meaning as linear fractionals over the involutive Banach algebra of operators with diagonal singularity. We show in this paper that the logic of quantum systems with diagonal singularity is not the conventional logic of (...) Hilbert space, because only finite combinations of prepositions are allowed. (shrink)

AN INVESTIGATION OF THE LAWS OF THOUGHT. CHAPTER I. NATURE AND DESIGN OF THIS WORK. . HPHE design of the following treatise is to investigate the ...