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Two types of universal proof systems for all variants of many-valued logics and some properties of them

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Abstract

Two types of propositional proof systems are described in this paper such that proof system for each variant of propositional many-valued logic can be presented in both of the described forms. The first of introduced systems is a Gentzen-like system, the second one is based on the generalization of the notion of determinative disjunctive normal form, formerly defined by first coauthor. Some generalization of Kalmar’s proof of deducibility for two-valued tautologies in the classical propositional logic gives us a possibility to suggest the easy method of proving the completeness for first type of described systems. The completeness of the second type one is received from its construction automatically. The introduced proof systems are “weak” ones with a “simple strategist” of proof search and we have investigated the quantitative properties, related to proof complexity characteristics in them as well. In particular, for some class of many-valued tautologies simultaneously optimal bounds (asymptotically the same upper and lower bounds for each proof complexity characteristic) are obtained in the systems, considered for some versions of many-valued logic.

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References

  1. Lukasiewicz, J.: O Logice Trojwartosciowej. Ruch filoseficzny (Lwow) 5, 169–171 (1920)

    Google Scholar 

  2. Post, E.: Introduction to a general theory of elementary propositions. Am. J. Math. 43, 163–185 (1921)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chubaryan, A.: Relative efficiency of some proof systems for classical propositional logic. In: Proceedings of NASA RA, Vol. 37,N5, 2002, and Journal of CMA (AAS), Vol. 37, N5, pp. 71–84 (2002)

  4. Mendelson, E.: Introduction to Mathematical Logic. Van Nostrand, Princeton (1975)

    MATH  Google Scholar 

  5. Aleksanyan, S., Chubaryan, A.: The polynomial bounds of proof complexity in Frege systems. Sib. Math. J. 50(2), 243–249 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chubaryan, A., Chubaryan, A., Sayadyan, S.: The relative efficiency of propositional proofs systems for classical and nonclassical propositional logic. Béziau, J.-Y., Costa-Leite, A. (eds.) Perspectives on Universal Logic, pp. 265-275(2007)

  7. Chubaryan An., Mnatsakanyan, A., Nalbandyan, H.: On some propositional proof system for modal logic, HAY, Oтечественная   наука в зпоху  изменениу:  постулаты  прошлого  и теории  нового времени,  часть10, 2(7), pp. 14–16 (2015)

  8. Chubaryan, A., Chubaryan, A., Nalbandyan, H., Sayadyan, S.: On some universal system for various propositional logics. Logic Colloquium: LC 2015 Annual European Summer Meeting of the Association for Symbolic Logic (ASL) University of Helsinki, 3–8 August 2015. The Bulletin of Symb. Logic 22(3), 391 (2015)

  9. Chubaryan, A.A., Tshitoyan, A.S., Khamisyan, A.A.: On some proof systems for many-valued logics and on proof complexities in it, (in Russian) National Academy of Sciences of Armenia. Reports 116(2), 18–24 (2016)

    Google Scholar 

  10. Chubaryan, A., Khamisyan, A., Tshitoyan, A.: On some systems for Łukasiewicz’s many-valued logic and its properties. Fundam. Sci. 8(8), 74–79 (2017)

    Google Scholar 

  11. Chubaryan, A., Khamisyan, A., Petrosyan, G.: On Some Systems for Two Versions of Many-Valued Logics and its Properties, p. 80. Lambert Academic Publishing (LAP), Beau Bassin, Mauritius (2017)

    Google Scholar 

  12. Chubaryan, A., Khamisyan, A.: Generalization of Kalmar’s proof of deducibility in two valued propositional logic into many valued logic. Pure Appl. Math. J. 6(2), 71–75 (2017). https://doi.org/10.11648/j.pamj.20170602.12

    Article  Google Scholar 

  13. Filmus, Y., Lauria, M., Nordstrom, J., Thapen, N., Ron-Zewi, N.: Space complexity in polynomial calculus. IEEE Conf Comput Complex (CCC) 2012, 334–344 (2012)

    MathSciNet  MATH  Google Scholar 

  14. Tshitoyan, A.: Bounds of proof complexities in some systems for many-valued logics, Isaac Scientific Publishing (ISP). J. Adv. Appl. Math. 2(3), 164–172 (2017)

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Authors and Affiliations

  1. Doctor of Physical and Mathematical Sciences, Yerevan State University, Yerevan, Armenia

    Anahit Chubaryan

  2. Yerevan State University, Yerevan, Armenia

    Artur Khamisyan

Authors
  1. Anahit Chubaryan
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  2. Artur Khamisyan
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Correspondence to Anahit Chubaryan.

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Chubaryan, A., Khamisyan, A. Two types of universal proof systems for all variants of many-valued logics and some properties of them. Iran J Comput Sci 2, 1–8 (2019). https://doi.org/10.1007/s42044-018-0015-4

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  • DOI: https://doi.org/10.1007/s42044-018-0015-4

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