International Journal of Fuzzy Logic and Intelligent Systems

  • 제16권3호
  • /
  • Pages.147-156
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  • 2016
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  • 1598-2645(pISSN)
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  • 2093-744X(eISSN)
한국지능시스템학회 (Korean Institute of Intelligent Systems)
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The Sound and Complete Gentzen Deduction System for the Modalized Łukasiewicz Three-Valued Logic

  • Cao, Cungen (Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences) ;
  • Sui, Yuefei (Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences)
  • 투고 : 2015.07.17
  • 심사 : 2016.09.22
  • 발행 : 2016.09.25
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초록

A modalized Łukasiewicz three-valued propositional logic will be proposed in this paper which there are three modalities [t]; [m]; [f] to represent the three values t; m; f; respectively. And a Gentzen-typed deduction system will be given so that the the system is sound and complete with respect to the Łukasiewicz three-valued semantics Ł$_3$, which are given in soundness theorem and completeness theorem.

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참고문헌

  1. A. Avron, "Natural 3-valued logics: characterization andproof theory," Journal of Symbolic Logic, vol. 56, no. 1, pp. 276-294, 1991. http://dx.doi.org/10.2307/2274919
  2. A. Avron, "Gentzen-type systems, resolution and tableaux," Journal of Automated Reasoning, vol. 10, no. 2, pp. 265-281,1993. http://dx.doi.org/10.1007/BF00881838
  3. D. A. Bochvar and M. Bergmann, "On a three-valued logical calculus and itsapplication to the analysis of the paradoxes of the classicalextended functional calculus," History and Philosophy ofLogic, vol. 2, no. 1-2, pp. 87- 112, 1981. http://dx.doi.org/10.1080/01445348108837023
  4. M. Fitting, "Many-valued modal logics II," FundamentaInformaticae, vol. 17, no. 1-2, pp. 55-73, 1992.
  5. S. Gottwald, A Treatise on Many-Valued Logics. Baldock: ResearchStudies Press, 2001.
  6. S. Gottwald, "Many-Valued Logic," Available http://plato.stanford.edu/entries/logic-manyvalued/
  7. R.Hahnle, "Advanced many-valued logics," in Handbook of Philosophical Logic, D. M. Gabbay and F. Guenthner, Eds. Dordrecht: Springer, 2001, pp. 297-395. http://dx.doi.org/10.1007/978-94-017-0452-6_5
  8. S. C. Kleene, "On notation for ordinal numbers," Journal of Symbolic Logic, vol. 3, no. 4, pp. 150-155,1938. http://dx.doi.org/10.2307/2267778
  9. W. Li, Mathematical Logic: Foundations for Information-Science. Basel: BirkhauserVerlag AG, 2010.
  10. J. Lukasiewicz, "O logicetrojwartosciowej [On threevalued logic]," Ruch filozoficzny, vol. 5, pp. 170-171, 1920.
  11. J. Lukasiewicz, "Selected Works," in Studies in Logic and the Foundations of Mathematics, L. Borkowski, Ed. Amsterdam:North-Holland and Warsaw, 1970.
  12. E. L. Post, "Determination of all closed systems of truthtables," Bulletin American Mathematical Society, vol. 26, pp. 437, 1920.
  13. E. L. Post, "Introduction to a general theory of elementarypropositions," American Journal of Mathematics, vol. 43, no. 3, pp. 163-185, 1921. http://dx.doi.org/10.2307/2370324
  14. A. Urquhart,"Basic many-valued logic," in Handbook of philosophical logic (vol. 2), D. M. Gabbay and F. Guenthner, Eds. Dordrecht: Springer, 2001, pp. 249-295. http://dx.doi.org/10.1007/978-94-017-0452-6 4
  15. W. Zhu, "Independence issues of the propositional connectivesin medium logic systems MP and MP," in AFriendly Collection of Mathematical Papers I. Changchun: Jilin University Press, 1990.
  16. J. Zhu, X. Xiao, and W. Zhu, "A survey of the developmentof medium logic calculus system and the research ofits semantics," in A Friendly Collection of Mathematical Papers I. Changchun: Jilin University Press, 1990.
  17. W. Zhu and X. Xiao, An Introduction to Foundations ofMathematics. Nanjing: Nanjing University Press, 1996.