Korean Journal of Logic (논리연구)

Korean Association for Logic (한국논리학회)
권호 표지

Algebraic Routley-Meyer-style semantics for the fuzzy logic MTL

퍼지 논리 MTL을 위한 대수적 루트리-마이어형 의미론

  • Yang, Eunsuk (Department of Philosophy & Institute of Critical Thinking and Writing, Chonbuk National University)
  • 양은석 (전북대학교 철학과, 비판적사고와논술연구소)
  • Received : 2018.07.22
  • Accepted : 2018.09.07
  • Published : 2018.10.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with Routley-Meyer-style semantics, which will be called algebraic Routley-Meyer-style semantics, for the fuzzy logic system MTL. First, we recall the monoidal t-norm logic MTL and its algebraic semantics. We next introduce algebraic Routley-Meyer-style semantics for it, and also connect this semantics with algebraic semantics.

이 글에서 우리는 대수적 루트리-마이어형 의미론이라고 불릴 의미론을 연구한다. 이를 위하여 먼저 퍼지 논리 체계 MTL과 대수적 의미론을 소개한다. 다음으로 이 체계를 위한 대수적 루트리-마이어형 의미론을 제공한 후, 이를 대수적 의미론과 연관 짓는다.

Keywords

References

  1. Cintula, P. (2006) "Weakly Implicative (Fuzzy) Logics I: Basic properties", Archive for Mathematical Logic, 45, pp. 673-704. https://doi.org/10.1007/s00153-006-0011-5
  2. Diaconescu, D. and Georgescu, G. (2007) "On the forcing semantics for monoidal t-norm based logic", Journal of Universal Computer Science, 13, pp. 1550-1572.
  3. Galatos, N., Jipsen, P., Kowalski, T., and Ono, H. (2007), Residuated lattices: an algebraic glimpse at substructural logics, Amsterdam, Elsevier.
  4. Hajek, P. (1998), Metamathematics of Fuzzy Logic, Amsterdam, Kluwer.
  5. Jenei, S and Montagna, F. (2002), "A Proof of Standard completeness for Esteva and Godo's Logic MTL", Studia Logica, 70, pp. 183-192. https://doi.org/10.1023/A:1015122331293
  6. Kripke, S. (1963). "Semantic analysis of modal logic I: normal modal propositional calculi", Zeitschrift für 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. Urquhart, A. (1986) "Many-valued logic". in D. Gabbay and F. Guenthner (eds.) Handbook of Philosophical Logic, vol. 3, Dordrecht: Reidel Publ Co, pp. 71-116.
  13. Yang, E. (2014a) "Algebraic Kripke-style semantics for weakening-free fuzzy logics", Korean Journal of Logic, 17 (1), pp. 181-195.
  14. 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
  15. Yang, E. (2014c) "Algebraic Kripke-style semantics for three-valued paraconsistent logic", Korean Journal of Logic, 17(3), pp. 441-460.
  16. Yang, E. (2016a) "Algebraic Kripke-style semantics for substructural fuzzy logics", Korean Journal of Logic, 19, pp. 295-322.
  17. Yang, E. (2016b) "Weakly associative fuzzy logics", Korean Journal of Logic, 19, pp. 437-461.
  18. Yang, E. (2016c) "Basic substructural core fuzzy logics and their extensions: Mianorm-based logics", Fuzzy Sets and Systems 276, pp. 43-58.
  19. Yang, E. (2017a) "Set-theoretic Kripke-style semantics for involutive monoidal t-norm (based) logics", Fhilosophical Ideas, 55(s), pp. 79-88.
  20. Yang, E. (2017b) "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
  21. Yang, E. (2018) "Algebraic Kripke-style semantics for weakly associative fuzzy logics", Korean Journal of Logic, 21(2), pp. 155-173.