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

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 107)

Abstract

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.

keywords

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

Notes

Acknowledgments

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

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

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

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