The Predicate System Based on Schweizer–Sklar t-Norm and Its Completeness

  • Li Qiao-Yan
  • Cheng Tao
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 107)


The aim of this chapter is the partial axiomatization for first-order predicate calculus formal system based on Schweizer–Sklar t-norm. By introducing the universal quantifier and existential quantifier, a predicate calculus formal deductive system \(\forall {\hbox{UL}}^{\ast}\) based on Schweizer–Sklar t-norm according to propositional calculus formal deductive system \({\hbox{UL}}^{\ast}\) based on Schweizer–Sklar t-norm is built up, moreover, the completeness of system \(\forall{\hbox{UL}}^{\ast}\) are proved. So it shows that the semantic and syntactic of system \(\forall {\hbox{UL}}^{\ast}\) are harmony.


Schweizer–Sklar t-norm Predicate calculus formal system Approximate reasoning 



This work is supported by Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 2010JK567).


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.School of ScienceXi’an Polytechnic UniversityXi’anChina

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