Foundations of Quantum Contextual Topos: Integrating Modality and Topos Theory in Quantum Logic
Jesse Werbow

TL;DR
This paper presents the Quantum Contextual Topos (QCT), a new framework combining topos theory and modal logic to better model the contextual and dynamic aspects of quantum mechanics.
Contribution
It introduces the QCT framework that embeds quantum contextuality within a topos-theoretic structure, integrating modal operators and classical logic.
Findings
QCT's internal logic aligns with classical propositional polymodal logic
Generalization of Stone's Representation Theorem for polymodal algebras
Demonstrates QCT's potential for modeling quantum systems more effectively
Abstract
This paper introduces the Quantum Contextual Topos (QCT), a novel framework that extends traditional quantum logic by embedding contextual elements within a topos-theoretic structure. This framework seeks to provide a classically-obedient tool for exploring the logical foundations of quantum mechanics. The QCT framework aims to address the limitations of classical quantum logic, particularly its challenges in capturing the dynamic and contextual nature of quantum phenomena. By integrating modal operators and classical propositional logic within a topos structure, the QCT offers a unified approach to modeling quantum systems. The main result of this work is demonstrating that the internal logic of QCT corresponds to a form of classical propositional polymodal logic. We do this by generalizing Stone's Representation Theorem for a specific case of polymodal algebras and their underlying…
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Taxonomy
TopicsAdvanced Algebra and Logic · Computability, Logic, AI Algorithms · Quantum Mechanics and Applications
