On Some Universal Propositional Proof Systems for Many-Valued Logic

Authors

  • Artur A. Khamisyan Yerevan State University

DOI:

https://doi.org/10.51408/1963-0049

Keywords:

Many-valued logic, Hilbert-like proof system, Uniform propositional proof system.

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

References

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

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

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.

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.

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.

А. Чубарян и А. Хамисян, Новый метод доказательства полноты пропозициональной системы трехзначной логики Лукасевича и его приложения, Evolutio, Естественные науки, Вып. 3, сс. 9-12, 2016.

A.Chubaryan, A.Khamisyan and G. Petrosyan, On Some Systems for Two Versions of Many-valued Logics and its Properties, Lambert Academic Publishing (LAP), 2017.

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Published

2020-07-10

How to Cite

Khamisyan, A. A. . (2020). On Some Universal Propositional Proof Systems for Many-Valued Logic. Mathematical Problems of Computer Science, 53, 21–28. https://doi.org/10.51408/1963-0049