Contextual logic for quantum systems
arXiv:quant-ph/0702023 · doi:10.1063/1.1819525
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