Can many-valued logic help to comprehend quantum phenomena?

TL;DR

This paper proposes that many-valued logic, specifically { extL}ukasiewicz logic, can better explain quantum phenomena and resolve paradoxes by modeling properties of quantum objects before measurement.

Contribution

It introduces a model of infinitely-valued { extL}ukasiewicz logic to describe quantum properties, challenging the traditional two-valued logic approach.

Findings

Reinterprets the GHZ paradox as an artifact of two-valued logic

Demonstrates the use of many-valued logic in quantum property description

Suggests a new logical framework for quantum phenomena

Abstract

Following {\L}ukasiewicz, we argue that future non-certain events should be described with the use of many-valued, not 2-valued logic. The Greenberger-Horne-Zeilinger `paradox' is shown to be an artifact caused by unjustified use of 2-valued logic while considering results of future non-certain events. Description of properties of quantum objects before they are measured should be performed with the use of propositional functions that form a particular model of infinitely-valued {\L}ukasiewicz logic. This model is distinguished by specific operations of negation, conjunction, and disjunction that are used in it.