Theory of generalized tautology in revised Kleene system

摘要

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 α~+ -tautology and generalized contradiction which are dual theory to generalized tautolo- (ii) gy have been introduced; (II) congruence partition about has been given in logic system W, W, (iii) W_k; (III) in logic system W_k, tautologies can be obtained by employing the upgrade algorithm at most (iv) [k+1/2] times to an arbitrary formula; (iv) in logic system W (W), tautologies cannot be obtained by (v) employing upgrade algorithm to non-tautologies with in finitely many times; (v) the deduction rule formula (ill.) holds in logic system W (W) .