Some properties of the roots of theories in propositional logic systems

Abstract

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, Łukasiewicz 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.