2014/08/22 by R. Salazar, Salazar, R., Cristian Jara-Figueroa +4
Computer Science · Physics and Astronomy · #Bayesian Modeling and Causal Inference #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1408.5308
arxiv created 2014/08/22 · openalex publication_date 2014/08/22 · arxiv updated 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive an analogue of the quantum total probability rule by constructing a probability theory based on paraconsistent logic. Bayesian probability theory is constructed upon classical logic and a desiderata, that is, a set of desired properties that the theory must obey. We construct a new probability theory following the desiderata of Bayesian probability theory but replacing the classical logic by paraconsistent logic. This class of logic has been conceived to handle eventual inconsistencies or contradictions among logical propositions without leading to the trivialisation of the theory. Within this Paraconsistent bayesian probability theory it is possible to deduce a new total probability rule which depends on the probabilities assigned to the inconsistencies. Certain assignments of values for these probabilities lead to expressions identical to those of Quantum mechanics, in particular to the quantum total probability rule obtained via symmetric informationally complete positive- operator valued measure.