JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2013, Vol. 43 ›› Issue (4): 87-92.

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Properties and applications of the roots of theories in propositional logic systems

ZHANG Jian-cheng, SU Lian-ta   

  1. School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
  • Received:2012-12-05 Online:2013-08-20 Published:2012-12-05

Abstract:

By means of theory of truth degrees of formulas, the properties of the generalized roots of theories in classical two-valued logic system, lukasiewicz propositional logic, Gdel propositional logic, and the R0-propositional logic were first studied according to deduction theorems. Then, it was proved that all consequences of a theory Γ, named D(Γ), were completely determined by its generalized root whenever Γ had a generalized root. Finally, a new algorithm of divergence degree, consistency degree, and Membership degree of  Γ-conclusion was obtained.

Key words: propositional logic system, generalized roots, divergence degree, consistency degree, membership degree

CLC Number: 

  • O141.1
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