Mutually exclusive nuances of truth

Nuances of truth represent a robust paradigm in the framework of many-valued logics [1]. The idea of nuancing states that a many-valued object is uniquely determined by some Boolean objects, its nuances, and it is called the determination principle. However, a many-valued object cannot be recovered only from its Boolean nuances. This idea goes back to Gr. C. Moisil [4] and it is mathematically expressed by a categorical adjunction between Boolean algebras and Lukasiewicz-Moisil algebras. Moisil’s determination principle cannot be extended for subalgebras: distinct LukasiewiczMoisil algebras can have the same Boolean algebra reduct.