Variant quantifiers in L₃-valued first-order logic

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

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