Quantum States as Virtual Singletons: Converting Duality into Symmetry

In a predicative framework from basic logic, defined for a model of quantum parallelism by sequents, we characterize a class of first order domains, called virtual singletons, which allows a generalization of the notion of duality, termed 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 states. So, despite not having sense in a traditional logical setting, symmetry can hide the peculiar advantage of quantum mechanics for the treatment of information.