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 with the Boolean sublattices of
the ortholattice of closed subspaces of the Hilbert space of the physical system.
Different from standard quantum logics, the contextual logic maintains a distributive
lattice structure and a good definition of implication as a residue of the
conjunction