A Formal Theory for Finite-Dimensional Possibilistic Quantum Mechanics

TL;DR

This paper introduces a classical first-order logical formalism for finite-dimensional quantum systems, enabling complete reasoning and new insights into hidden variable models within quantum mechanics.

Contribution

It develops a complete, classical first-order logic framework for finite-dimensional quantum systems, contrasting with traditional quantum logic approaches.

Findings

The formalism is complete, fully determining quantum system behavior.

Provides a characterization of models, offering insights into hidden variable theories.

Bridges quantum logic with classical model theory techniques.

Abstract

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of model theory in our study. In particular, we show that our formal theory is complete, meaning that it entirely determines the behaviour of quantum systems. Moreover, we provide a characterization of the models of our formal theory, thus providing new insights in the study of hidden variable models of quantum theory.