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Partitions of F(S) and its Application in Gdel's Logic System

WU Hong-bo

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Abstract

Theory of generalized tautology in logic system ,W,W k is generalized, both of which was introduced in 1997 by professor Wangguo-jun,and an application of it is made to Gdel's logic system. The main results are:In logic system ,G, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times. In logic system G n, tautologies can be get by using upgrade algorithm to an arbitrary formula of F(S) at most n-1 times. Congruence partitions about  on F(S) have been given in logic system ,G,G n, respectively by utilizing the concepts of accessible generalized tautology and α-contradiction

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What this paper is about

Theory of generalized tautology in logic system ,W,W k is generalized, both of which was introduced in 1997 by professor Wangguo-jun,and an application of it is made to Gdel's logic system. The main results are:In logic system ,G, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times. In logic system G n, tautologies can be get by using upgrade algorithm to an arbitrary formula of F(S) at most n-1 times. Congruence partitions about  on F(S) have been given in logic system ,G,G n, respectively by utilizing the concepts of accessible generalized tautology and α-contradiction

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Available abstract

Theory of generalized tautology in logic system ,W,W k is generalized, both of which was introduced in 1997 by professor Wangguo-jun,and an application of it is made to Gdel's logic system. The main results are:In logic system ,G, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times. In logic system G n, tautologies can be get by using upgrade algorithm to an arbitrary formula of F(S) at most n-1 times. Congruence partitions about  on F(S) have been given in logic system ,G,G n, respectively by utilizing the concepts of accessible generalized tautology and α-contradiction

Key concepts: Tautology (logic), Mathematics, Upgrade, Discrete mathematics, Algorithm, Arithmetic, Zeroth-order logic, Theoretical computer science

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