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2017 | 26 | 2 | 197–206
Article title

Natural Deduction for Three-Valued Regular Logics

Content
Title variants
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EN
Abstracts
EN
In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermediate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction systems are built only for strong Kleene’s logic both with one (A. Urquhart, G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi, A. Tamminga). The purpose of this paper is to provide natural deduction systems for weak and intermediate regular logics both with one and two designated values.
Year
Volume
26
Issue
2
Pages
197–206
Physical description
Dates
published
2017-06-15
Contributors
References
  • Bochvar, D.A., “On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus”, History and Philosophy of Logic, 2 (1981): 87–112. English translation of Bochvar’s paper of 1938. DOI: 10.1080/01445348108837023
  • Fitting, M., “Kleene’s three valued logics and their children”, Fundamenta Informaticae, 20 (1992): 113–131.
  • Karpenko, A.S., The Development of Many-Valued Logic (in Russian), LKI, 2010.
  • Kleene, S.C., “On a notation for ordinal numbers”, The Journal of Symbolic Logic, 3 (1938): 150–155. DOI: 10.2307/2267778
  • Kleene, S.C., Introduction to Metamathematics, Sixth Reprint, Wolters-Noordhoff Publishing and North-Holland Publishing Company, 1971.
  • Komendantskaya, E.Y., “Functional expressibility of regular Kleene’s logics” (in Russian), Logical Investigations, 15 (2009): 116–128.
  • Kooi, B., and A. Tamminga, “Completeness via correspondence for extensions of the logic of paradox”, The Review of Symbolic Logic, 5 (2012): 720–730. DOI: 10.1017/S1755020312000196
  • Łukasiewicz, J., “On three-valued logic”, pages 87–88 in Selected Works, L. Borkowski (ed.), Amsterdam, North-Holland Publishing Company, 1997 (English translation of Łukasiewicz’s paper of 1920).
  • Mendelson, E., Introduction to Mathematical Logic, Fourth Edition, Chapman & Hall, 1997.
  • Petrukhin, Y.I., “Correspondence analysis for first degree entailment”, Logical Investigations, 22, 1 (2016): 108–124.
  • Priest, G., “Paraconsistent logic”, in Handbook of Philosophical Logic, Second Edition, Vol. 6, M. Gabbay and F. Guenthner (eds.), Dordrecht, Kluwer, 2002. DOI: 10.1007/978-94-017-0460-1_4
  • Tamminga, A., “Correspondence analysis for strong three-valued logic”, Logical Investigations, 20 (2014): 255–268.
  • Tomova, N.E., “About four-valued regular logics” (in Russian), Logical Investigations, 15 (2009): 223–228.
  • Urquhart, A., “Basic many-valued logic”, in Handbook of Philosophical Logic, Second Edition, Vol. 2, M. Gabbay and F. Guenthner (eds.), Dordrecht, Kluwer, 2001. DOI: 10.1007/978-94-017-0452-6_4
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-81779f55-5086-4f24-a6e3-ff4e5356380c
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