Generalization of Kalmar’s Proof of Deducibility in Two Valued Propositional Logic into Many Valued Logic
Pure and Applied Mathematics Journal
Volume 6, Issue 2, April 2017, Pages: 71-75
Received: Feb. 13, 2017; Accepted: Mar. 15, 2017; Published: Mar. 22, 2017
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Authors
Chubaryan Anahit, Department of Informatics and Applied Mathematics, Yerevan State University and Russian-Armenian University, Yerevan, Armenia
Khamisyan Artur, Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, Armenia
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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.
Keywords
Many-Valued Logics, Hilbert-Style Axiomatic Systems, Completeness of Formal System
To cite this article
Chubaryan Anahit, Khamisyan Artur, Generalization of Kalmar’s Proof of Deducibility in Two Valued Propositional Logic into Many Valued Logic, Pure and Applied Mathematics Journal. Vol. 6, No. 2, 2017, pp. 71-75. doi: 10.11648/j.pamj.20170602.12
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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