Eigenlogic and Probabilistic Inference; when Bayes meets Born

TL;DR

This paper explores how Eigenlogic projection operators can be used to unify logical inference with probabilistic reasoning, drawing connections between quantum mechanics and Bayesian inference.

Contribution

It introduces a novel probabilistic interpretation of Eigenlogic operators using the Born rule, bridging quantum logic and Bayesian probability.

Findings

Eigenlogic operators represent logical connectives and models.

Probabilities are computed via the quantum mean value (Born rule).

The approach links quantum mechanics with Bayesian inference.

Abstract

This paper shows how inference is treated within the context of Eigenlogic projection operators in linear algebra. In Eigenlogic operators represent logical connectives, their eigenvalues the truth-values and the associated eigenvectors the logical models. By extension, a probabilistic interpretation is proposed using vectors outside the eigensystem of the Eigenlogic operators. The probability is calculated by the quantum mean value (Born rule) of the logical projection operators. We look here for possible connections between the Born rule in quantum mechanics and Bayes' theorem from probability theory and show that Eigenlogic offers an innovative approach to address the probabilistic version of logical inference (material implication) in a quantum context.