Contextual logic for quantum systems

Abstract

In this work we build a quantum logic that allows us to refer to physical magnitudes pertaining to different contexts from a fixed one without the contradictions with quantum mechanics expressed in no-go theorems. This logic arises from considering a sheaf over a topological space associated to the Boolean sublattices of the ortholattice of closed subspaces of the Hilbert space of the physical system. Differently to standard quantum logics, the contextual logic maintains a distributive lattice structure and a good definition of implication as a residue of the conjunction.

16 pages, no figures

References in corpus (2)

• Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets
• An obstruction based approach to the Kochen-Specker theorem

Cited by in corpus (8)

• The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations
• Non-deterministic semantics for quantum states
• Fuzzy Propositional Logic Associated with Quantum Computational Gates
• Modal-type orthomodular logic
• Scopes and Limits of Modality in Quantum Mechanics
• Many worlds and modality in the interpretation of quantum mechanics: an algebraic approach
• A Topological Study of Contextuality and Modality in Quantum Mechanics
• Physical properties as modal operators in the topos approach to quantum mechanics