Many-Valued Interpretation of the Logic of Quantum Mechanics

Hans Reichenbach

Peter Mittelstaedt

Michael Dickson

This paper proposes a logic, motivated by modal interpretations, in which every quantum mechanics propositions has a truth-value. This logic is completely classical, hence violates the conditions of the Kochen-Specker theorem. It is shown how the violation occurs, and it is argued that this violation is a natural and acceptable consequence of modal interpretations. It is shown that despite its classicality, the proposed logic is empirically indistinguishable from quantum logic.

Jarosław Pykacz

Jarosław Pykacz

A many–valued logic from an old neglected Lukasiewicz paper is adopted to describe results of physical (esp. quantum) experiments. Truth–values of propositions are interpreted as probabilities of their experimental confirmation. It is shown that the Lindenbaum algebra of the obtained logic is an orthomodular partially ordered set, i.e. a “quantum logic” in the Birkhoff–von Neumann sense. Short outline of the historical development of applications of many–valued logics in foudations of quantum mechanics is given.

Jarosław Pykacz