On Some Universal Propositional Proof Systems for Many-Valued Logic

Author:

Khamisyan Artur1

Affiliation:

1. Yerevan State University

Abstract

Some uniform Hilbert-like propositional proof system is suggested for all versions of many-valued logic to apply them to 3 versions of 3-valued logic, two of which have only one designated value, and the last one has two designated values

Publisher

Institute for Informatics and Automation Problems - NAS RA

Subject

General Medicine

Reference7 articles.

1. J. Lukasiewicz, “O Logice Trójwartósciowej”, Ruch Filozeficzny English translation: On three valued-logic, vol. 5, pp. 169-171, 1920.

2. E. Mendelson, Introduction to Mathematical Logic, Van Nostrand, Princeton, 1975.

3. A. A. Chubaryan, A. S. Tshitoyan and A. A. Khamisyan, “On some proof systems for many-valued logics and on proof complexities in it”, (in Russian) Reports of NASA RA, vol. 116, no. 2, pp. 18-24, 2016.

4. A. Chubaryan and A. Khamisyan, “Generalization of Kalmar’s proof of deducibility in two valued propositional logic into many valued logic”, Pure and Applied Mathematics Journal, doi: 10.116448/j.pamj. 20170602.12, vol. 6, no. 2, pp. 71-75, 2017.

5. A. Chubaryan, A. Khamisyan and A. Tshitoyan, “On some systems for Łukasiewicz’s many-valued logic and its properties”,FundamentalisScientiam, vol. 8, no. 8, Spain, pp. 74-79, 2017.

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