This paper is a complement and extension of the theory of generalized tautology which was first proposed by Wang Guojun in revised Kleene system, Some interesting results are obtained: (i) accessible *+ -tautology and generalized contradiction which are dual theory to generalized tautology have been introduced; (ii) congruence partition about has been given in logic system W, W, Wk; (iii) in logic system Wk , tautologies can be obtained by employing the upgrade algorithm at most[k+1/2] times to an arbitrary formula; (iv) in logic system W( W) , tautologies cannot be obtained by employing upgrade algorithm to non-tautologies within finitely many times; (v) the deduction rule ( [ (1/2)+ ] - MP] ho|ds in logic system W( W) . This paper is a complement and extension of the theory of generalized tautology which was first proposed by Wang Guojun in revised Kleene system, Some interesting results are obtained: (i) accessible * + -tautology and generalized contradiction which are dual theory to generalized tautology have (ii) congruence partition about has been given in logic system W, W, Wk; (iii) in logic system Wk, tautologies can be obtained by employing the upgrade algorithm at most [k + 1/2] times to an arbitrary formula; (iv) in logic system W (W), tautologies can not be obtained by employing upgrade upgrade algorithm to non-tautologies within finitely many times; (v) the deduction rule ([(1/2) +] - MP] ho | ds in logic system W (W).