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2000•Journal of Sichuan UniversityRequires access

THEORY OF GENERALIZED TAUTOLOGY IN GAINSE-RESCHER'S LOGIC SYSTEM

Wu Hong

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Abstract

Theory of generalized tautology in Logic system ,W,W k is generalized, both of which is introduced by professor Wang Guo Jun, and an application of it is made to Gainse Rescher's Logic System. The main results are:In logic system r,G r, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times; In logic system S 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 r,G r,S 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 Guo Jun, and an application of it is made to Gainse Rescher's Logic System. The main results are:In logic system r,G r, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times; In logic system S 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 r,G r,S 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 Guo Jun, and an application of it is made to Gainse Rescher's Logic System. The main results are:In logic system r,G r, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times; In logic system S 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 r,G r,S n, respectively by utilizing the concepts of accessible generalized tautology and α contradiction.

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

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