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Variant quantifiers in L3-valued first-order logic

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Abstract

Traditional first-order logic has four definitions for quantifiers, which are defined by universal and existential quantifiers. In L3-valued (three-valued) first-order logic, there are eight kinds of definitions for quantifiers; and corresponding Gentzen deduction systems will be given and their soundness and completeness theorems will be proved.

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Correspondence to Yuefei Sui.

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Wei Li is a PhD, Professor, PhD supervisor, and Academician of Chinese Academy of Sciences, China. He is a professor in the School of Computer Science and Engineering, Beihang University, China. His main research interests include computer science theory and software foundation, theory and practice of unstructured data, and analysis and processing of big data.

Yuefei Sui is a PhD, Professor, PhD supervisor, and a member of China Computer Federation. He is a professor in the Institute of Computing Technology, Chinese Academy of Sciences, and is a professor in School of Computer Science and Technology, University of Chinese Academy of Sciences, China. His main research interests include foundation of large-scale knowledge process and mathematical logic.

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Li, W., Sui, Y. Variant quantifiers in L3-valued first-order logic. Front. Comput. Sci. 15, 155403 (2021). https://doi.org/10.1007/s11704-020-7399-7

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