Speakable in quantum mechanics: babbling on

TL;DR

This paper derives an intuitionistic quantum logic, extends it to a classical logic framework, and explores probabilistic models, aiming to bridge quantum logic with classical probability theories.

Contribution

It introduces a classical logic extension of quantum logic and develops a probabilistic framework based on Rényi's conditional probability spaces.

Findings

Extension of quantum logic to classical logic CL_QM

Initial steps towards a probabilistic framework using Rényi's spaces

Comparison with traditional quantum probability frameworks

Abstract

This paper consists of a short version of the derivation of the intuitionistic quantum logic L_QM (which was originally introduced by Caspers, Heunen, Landsman and Spitters). The elaboration consists of extending this logic to a classical logic CL_QM. Some first steps are then taken towards setting up a probabilistic framework based on CL_QM in terms of R\'enyi's conditional probability spaces. Comparisons are then made with the traditional framework for quantum probabilities.