  In a predicative framework from basic logic, defined for a model of quantum
parallelism by sequents, we characterize a class of first order domains, termed
{\em virtual singletons}, which allows a generalization of the notion of
duality, termed {\em symmetry}. Although consistent with the classical notion
of duality, symmetry creates an environment where negation has fixed points,
for which the direction of logical consequence is irrelevant. Symmetry can
model Bell's states. So, despite its nonsense in a traditional logical setting,
symmetry can hide the peculiar advantage for the treatment of information, that
is proper of quantum mechanics.
