# 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)

## 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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