A discussion on the origin of quantum probabilities

arXiv:1211.4952We 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-Kolmogorovian 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). © 2013 Elsevier Inc.This work was partially supported by the grants PIP No 6461/05 and 1177 (CONICET). Also by the projects FIS2008-00781/FIS (MICINN) - FEDER (EU) (Spain, EU). The contribution of F. Holik to this work was done during his postdoctoral stance (CONICET) at Universidad Nacional de La Plata, Instituto de Física (IFLP-CCT-CONICET), C.C.727, 1900 La Plata, Argentina.N