Theory of generalized tautology in revised Kleene system |
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Authors: | WU Hongbo |
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Affiliation: | Department of Mathematics, Sichuan University, Chengdu 610064, China;Tangshan Normal College, |
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Abstract: | 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 mostk+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) . |
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Keywords: | logic system accessibleα +-tautology upgrade algorithm α -contradiction partition |
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