The Many-Valued Logic of Quantum Mechanics
Jarosław Pykacz · International Journal of Theoretical Physics · 2019
Abstract It is shown that any quantum logic in the Birkhoff - von Neumann sense that possesses an ordering set of probability measures can be isomorphically represented as a particular kind of infinite-valued Łukasiewicz logic with partially defined conjunction and disjunction. It is argued that such non-classical features of BvN quantum logic as lack of distributivity or validity of the orthomodular law follow from properties of Łukasiewicz conjunction and disjunction.