Tautologies in some lattice-valued logic systems

In this paper, the tautologies in some lattice-valued logic systems whose truth-values fields are lattices are formed by direct product of two lattice implication algebras, /spl alpha/-tautologies and F-tautologies are also discussed. As two examples, the tautologies in lattice-valued systems of L/sub 4/P (X) and L/sub 6/P (X) are discussed.