Korean Journal of Logic (논리연구)

Korean Association for Logic (한국논리학회)
권호 표지

Algebraic Kripke-Style Semantics for Weakly Associative Fuzzy Logics

약한 결합 원리를 갖는 퍼지 논리를 위한 대수적 크립키형 의미론

  • Yang, Eunsuk (Department of Philosophy & Institute of Critical Thinking and Writing, Chonbuk National University)
  • 양은석 (전북대학교 철학과, 비판적사고와논술연구소)
  • Received : 2018.03.12
  • Accepted : 2018.04.24
  • Published : 2018.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with Kripke-style semantics, which will be called algebraic Kripke-style semantics, for weakly associative fuzzy logics. First, we recall algebraic semantics for weakly associative logics. W next introduce algebraic Kripke-style semantics, and also connect them with algebraic semantics.

이 글에서 우리는 (곱 연언 &의) 약한 형식의 결합 원리를 갖는 퍼지 논리를 위한 대수적 크립키형 의미론을 연구한다. 이를 위하여 먼저 약한 결합 원리를 갖는 퍼지 논리의 대수적 의미론을 소개한다. 다음으로 이 체계들을 위한 대수적 크립키형 의미론을 제공한 후, 이를 대수적 의미론과 연관 짓는다.

Keywords

References

  1. Cintula, P., Horcik, R., and Noguera, C. (2013), "Non-associative substructural logics and their semilinear extensions: axiomatization and completeness properties", Review of Symbol. Logic, 12, pp. 394-423.
  2. Cintula, P., Horcik, R., and Noguera, C. (2015), "The quest for the basic fuzzy logic", Mathematical Fuzzy Logic, P. Hajek (Ed.), Springer.
  3. Cintula, P. and Noguera, C. (2011), A general framework for mathematical fuzzy logic, Handbook of Mathematical Fuzzy Logic, vol 1, P. Cintula, P. Hajek, and C. Noguera (Eds.), London, College publications, pp. 103-207.
  4. Galatos, N., Jipsen, P., Kowalski, T., and Ono, H. (2007), Residuated lattices: an algebraic glimpse at substructural logics, Amsterdam, Elsevier.
  5. Horcik, R. (2011), Algebraic semantics: semilinear FL-algebras, Handbook of Mathematical Fuzzy Logic, vol 1, P. Cintula, P. Hajek, and C. Noguera (Eds.), London, College publications, pp. 283-353.
  6. Kripke, S. (1963). "Semantic analysis of modal logic I: normal modal propositional calculi", Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9, pp. 67-96. https://doi.org/10.1002/malq.19630090502
  7. Kripke, S. (1965a) "Semantic analysis of intuitionistic logic I", in J. Crossley and M. Dummett (eds.) Formal systems and Recursive Functions, Amsterdam: North-Holland Publ Co, pp. 92-129.
  8. Kripke, S. (1965b) "Semantic analysis of modal logic II", in J. Addison, L. Henkin, and A. Tarski (eds.) The theory of models, Amsterdam: North-Holland Publ Co, pp. 206-220.
  9. Montagna, F. and Ono, H. (2002) "Kripke semantics, undecidability and standard completeness for Esteva and Godo's Logic MTL${\forall}$", Studia Logica, 71, pp. 227-245. https://doi.org/10.1023/A:1016500922708
  10. Montagna, F. and Sacchetti, L. (2003) "Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 49, pp. 629-641. https://doi.org/10.1002/malq.200310068
  11. Montagna, F. and Sacchetti, L. (2004) "Corrigendum to "Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 50, pp. 104-107. https://doi.org/10.1002/malq.200310081
  12. Yang, E. (2009) "Non-associative fuzzy-relevance logics: strong t-associative monoidal uninorm logics", Korean Journal of Logic, 12/1, pp. 89-110.
  13. Yang, E. (2012) "Kripke-style semantics for UL", Korean Journal of Logic, 15 (1), pp. 1-15.
  14. Yang, E. (2014a) "Algebraic Kripke-style semantics for weakening-free fuzzy logics", Korean Journal of Logic, 17 (1), pp. 181-195.
  15. Yang, E. (2014b) "Algebraic Kripke-style semantics for relevance logics", Journal of Philosophical Logic, 43, pp. 803-826. https://doi.org/10.1007/s10992-013-9290-6
  16. Yang, E. (2015a) "Weakening-free, non-associative fuzzy logics: micanorm-based logics", Fuzzy Sets and Systems, 276, pp. 43-58. https://doi.org/10.1016/j.fss.2014.11.020
  17. Yang, E. (2015b) "Some an axiomatic extension of the involutive micanorm logic IMICAL", Korean Journal of Logic, 18/2, pp. 197-215.
  18. Yang, E. (2016a) "Algebraic Kripke-style semantics for substructural fuzzy logics", Korean Journal of Logic 19, pp. 295-322.
  19. Yang, E. (2016b) "Weakly associative fuzzy logics", Korean Journal of Logic 19, pp. 437-461.
  20. Yang, E. (2016c) "Basic substructural core fuzzy logics and their extensions: Mianorm-based logics", Fuzzy Sets and Systems 276, pp. 43-58.
  21. Yang, E. (2017a) "Involutive basic substructural core fuzzy logics: Involutive mianorm-based logics", Fuzzy Sets and Systems, 320, pp. 1-16. https://doi.org/10.1016/j.fss.2017.03.013
  22. Yang, E. (2017b) "Some axiomatic extensions of the involutive mianorm Logic IMIAL", Korean Journal of Logic 20, pp. 295-322.
  23. Yang, E. (2017c) "A non-associative generalization of continuous t-norm-based logics", Journal of Intelligent & Fuzzy Systems 33, pp. 3743-3752. https://doi.org/10.3233/JIFS-17623