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Theory of Generalized Tautology in Godel’s Logic System

Wu Hong

Open publisher page 1 citations

Abstract

Theory of generalized tautology in Logic system ,W,W k is generalized, both of which is introduced by Professor Wang Guojun, and an application of it is made to Go o ¨del'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 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 is introduced by Professor Wang Guojun, and an application of it is made to Go o ¨del'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 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 is introduced by Professor Wang Guojun, and an application of it is made to Go o ¨del'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 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, Discrete mathematics, Algorithm, Algebra over a field, Zeroth-order logic, Theoretical computer science, Multimodal logic

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