Generalization of Kalmar’s Proof of Deducibility in Two Valued Propositional Logic into Many Valued Logic

IF 0.2 Q4 MATHEMATICS
Chubaryan Anahit, Khamisyan Artur
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引用次数: 6

Abstract

This paper focuses on the problem of constructing of some standard Hilbert style proof systems for any version of many valued propositional logic. The generalization of Kalmar’s proof of deducibility for two valued tautologies inside classical propositional logic gives us a possibility to suggest some method for defining of two types axiomatic systems for any version of 3-valued logic, completeness of which is easy proved direct, without of loading into two valued logic. This method i) can be base for direct proving of completeness for all well-known axiomatic systems of k-valued (k≥3) logics and may be for fuzzy logic also, ii) can be base for constructing of new Hilbert-style axiomatic systems for all mentioned logics.
二值命题逻辑中Kalmar的可演绎性证明推广到多值逻辑
本文研究了多值命题逻辑的任意版本的标准Hilbert式证明系统的构造问题。经典命题逻辑中卡尔玛二值重言式的可演绎性证明的推广,给我们提供了一种定义任意三值逻辑的两种类型公理系统的方法,它的完备性不需要加载到二值逻辑中,而易于直接证明。该方法可作为直接证明所有已知的k值(k≥3)逻辑公理系统完备性的基础,也可用于模糊逻辑,可作为构造所有上述逻辑的新的hilbert式公理系统的基础。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.60
自引率
0.00%
发文量
2
期刊介绍: The “Italian Journal of Pure and Applied Mathematics” publishes original research works containing significant results in the field of pure and applied mathematics.
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