Some properties of the roots of theories in propositional logic systems

摘要

Some properties of the roots of theories, and the relationship between the sets D(Γ) of all conclusions of two different theories in the classical propositional logic system, Lukasiewicz propositional logic system, and the R_0-propositional logic system are studied. It is proved that D(Γ) is completely determined by its root whenever Γ has a root, and the construction of the roots is given.