On the logical structure of quantum mechanics

Gottfried T. Rüttimann

Enrico G. Beltrametti, Gianni Cassinelli

Andréa Oldofredi, Gabriele Carcassi, C. Aidala

Daniel J. Lehmann, Kurt Engesser, Dov M. Gabbay

Pitsri Atisoontornkul, Preedeeporn Limcharoeri

Several attempts have been made to establish the logical structure of quantum mechanics on an axiomatic foundation. It has been shown that, whereas the logical structure of the propositional calculus of classical mechanics is that of a Boolean lattice, the logical structure of the propositional calculus of quantum mechanics is non-Boolean. Moreover, a probability model of a quantum system, namely, the quantum probability model, has a mathematical structure completely different from that of the Kolmogorovian probability model, which is the standard probability model of a classical system. These results, which are still controversial, are analysed and put in critical perspective.

Pawe l Sadowski, Andrzej Trybulec, Konrad Raczkowski

Summary. In this article we present the logical structure given by four axioms of Mackey [3] in the set of propositions of Quantum Mechanics. The equivalence relation (PropRel(Q)) in the set of propositions (Prop Q) for given Quantum Mechanics Q is considered. The main text for this article is [6] where the structure of quotient space and the properties of equivalence relations, classes and partitions are studied.