A discussion on the origin of quantum probabilities

TL;DR

This paper explores the foundational origin of quantum probabilities through non-boolean propositional structures, applying Cox's method to develop a generalized framework for non-Kolmogorovian probability measures in quantum mechanics.

Contribution

It introduces a novel application of Cox's method to non-distributive lattices, providing an alternative formulation of quantum probabilities within a generalized propositional framework.

Findings

Developed a generalized framework for probabilities in non-distributive lattices.

Presented an alternative formulation of quantum probability measures.

Extended Cox's method to non-boolean propositional structures.

Abstract

We study the origin of quantum probabilities as arising from non-boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorvian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).