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

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Computer, Informatics, Cybernetics and Applications

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

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. School of Science, Xi’an Polytechnic University, Xi’an, 710048, China

    Li Qiao-Yan & Cheng Tao

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  1. Li Qiao-Yan
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  2. Cheng Tao
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Corresponding author

Correspondence to Li Qiao-Yan .

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Editors and Affiliations

  1. Chinese Academy of Engineering, Beijing, China, People's Republic

    Xingui He

  2. Zhejiang Gongshang University, Beijing, China, People's Republic

    Ertian Hua

  3. Zhejiang Gongshang University, Hangzhou, China, People's Republic

    Yun Lin

  4. , School of Automation, Wuhan University of Technology, East District of Wuhan University, Luoshi Road 122, Wuhan, 4300, China, People's Republic

    Xiaozhu Liu

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Qiao-Yan, L., Tao, C. (2012). The Predicate System Based on Schweizer–Sklar t-Norm and Its Completeness. In: He, X., Hua, E., Lin, Y., Liu, X. (eds) Computer, Informatics, Cybernetics and Applications. Lecture Notes in Electrical Engineering, vol 107. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1839-5_22

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  • DOI: https://doi.org/10.1007/978-94-007-1839-5_22

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-1838-8

  • Online ISBN: 978-94-007-1839-5

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