Variant quantifiers in <strong>L</strong><sub>3</sub>-valued first-order logic

doi:10.1007/s11704-020-7399-7

Front. Comput. Sci.

2021, Vol. 15

Issue (5) : 155403 https://doi.org/10.1007/s11704-020-7399-7

RESEARCH ARTICLE

Variant quantifiers in L₃-valued first-order logic

Wei LI¹, Yuefei SUI^2,³(

)

¹. State Key Laboratory of Software Development Environment, Beihang University, Beijing 100083, China
². Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
³. School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China

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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.

Keywords L₃-valued (three-valued) first-order logic sequent quantifier soundness theorem completeness theorem

Corresponding Author(s): Yuefei SUI

Just Accepted Date: 18 December 2020 Issue Date: 11 June 2021

Cite this article:

Wei LI,Yuefei SUI. Variant quantifiers in L₃-valued first-order logic[J]. Front. Comput. Sci., 2021, 15(5): 155403.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-020-7399-7
https://academic.hep.com.cn/fcs/EN/Y2021/V15/I5/155403

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