Logos & Episteme Logos & Episteme
Pierre UZAN
ABSTRACT: Due to the failure of the classical principles of bivalence and verifunctionality, the logic of experimental propositions relative to quantum systems cannot be interpreted in Boolean algebras. However, we cannot say neither that this logic is captured by orthomodular lattices, as claimed by many authors along the line of Birkhoff’s and von Neumann’s standard approach. For the alleged violation of distributivity is based on the possibility of combining statements relative to complementary contexts, which does not refer to any experience and, consequently, has no meaning. Indeed, quantum logic should be interpreted in partial, transitive Boolean algebras whose compatibility relation limits the application of the connectives within each of its Boolean sub-algebras, which refer to partial, classical descriptions. Moreover, this approach of quantum logic makes it possible to deal with composite systems, which was not possible to do within the standard approach, and then to deal with the fundamental notion of quantum entanglement. The latter notion can be represented by a series of axioms of the object language that restrict the set of experimental statements bearing on a composite system, while its close link to the notion of complementarity can be expressed in the metalanguage.
