Korean Journal of Logic (논리연구)

Korean Association for Logic (한국논리학회)
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Set-Theoretical Kripke-Style Semantics for an Extension of HpsUL, CnHpsUL*

CnHpsUL*을 위한 집합 이론적 크립키형 의미론

  • Yang, Eunsuk (Department of Philosophy & Institute of Critical Thinking and Writing, Chonbuk National University)
  • 양은석 (전북대학교 철학과, 비판적사고와논술연구소)
  • Received : 2017.11.21
  • Accepted : 2018.01.05
  • Published : 2018.02.28
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Abstract

This paper deals with non-algebraic Kripke-style semantics, i.e, set-theoretical Kripke-style semantics, for weakening-free non-commutative fuzzy logics. We first recall an extension of the pseudo-uninorm based fuzzy logic HpsUL, $CnHpsUL^*$. We next introduce set-theoretical Kripke-style semantics for it.

이 글에서 우리는 약화 없는 비교환적인 퍼지 논리의 비대수적 크립키형 의미론 즉 집합 이론적 크립키형 의미론을 다룬다. 이를 위하여 먼저 우리는 가-유니놈에 기반한 퍼지 논리 HpsUL의 한 확장 체계인 $CnHpsUL^*$을 소개한다. 다음으로 CnHpsUL*을 위한 집합 이론적 크립키형 의미론을 소개한다.

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. Cintula, P., Horcik, R., and Noguera, C. (2013), "Non-associative substructural logics and their semilinear extensions: axiomatization and completeness properties", Review of Symbolic Logic 6: pp. 394-423. https://doi.org/10.1017/S1755020313000099
  3. Cintula, P., Horcik, R., and Noguera, C. (2015), "The quest for the basic fuzzy logic", in F. Montagna (ed.) Petr Hajek on Mathematical Fuzzy Logic, Dordrecht: Springer, pp. 245-290.
  4. Cintula, P. and Noguera, C. (2011), A general framework for mathematical fuzzy logic, in P. Cintula, P. Hájek, and C. Noguera (eds.) Handbook of Mathematical Fuzzy Logic, vol 1, London: College publications, pp. 103-207.
  5. Diaconescu, D. (2010), "Kripke-style semantics for non-commutative monoidal t-norm logic", Journal of Multiple-Valued Logic and Soft Computing 16: pp. 247-263.
  6. 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.
  7. Esteva, F. and Godo, L. (2001), "Monoidal t-norm based logic: towards a logic for left-continuous t-norms", Fuzzy Sets and Systems 124: pp. 271-288. https://doi.org/10.1016/S0165-0114(01)00098-7
  8. Hajek, P. (2003a), "Fuzzy logics with noncommutative conjunction", Journal of Logic and Computation 13: pp. 469-479. https://doi.org/10.1093/logcom/13.4.469
  9. Hajek, P. (2003b), "Observations on non-commutative fuzzy logic", Soft Computing 8: pp. 38-43. https://doi.org/10.1007/s00500-002-0246-y
  10. Metcalfe, G. and Montagna, F. (2007), "Substructural Fuzzy Logics", Journal of Symbolic Logic 72: pp. 834-864. https://doi.org/10.2178/jsl/1191333844
  11. Metcalfe, G., Olivetti, N., and Gabbay, D. (2009), Proof Theory for Fuzzy Logics, Springer.
  12. 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
  13. 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
  14. 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
  15. Tsinakis, C. and Blount, K. (2003), "The structure of residuated lattices", International Journal of Algebra and Computation 13: pp. 437-461. https://doi.org/10.1142/S0218196703001511
  16. Wang, S. (2013) "Logics for residuated pseudo-uninorms and their residua", Fuzzy Sets and Systems 218: pp. 24-31. https://doi.org/10.1016/j.fss.2012.11.018
  17. Wang, S. and Zhao, B. (2009), "HpsUL is not the logic of pseudo-uninorms and their residua", Logic Journal of the IGPL 17: pp. 413-419. https://doi.org/10.1093/jigpal/jzp023
  18. Yang, E. (2012), "Kripke-style semantics for UL", Korean Journal of Logic 15 (1): pp. 1-15.
  19. Yang, E. (2014a), "Algebraic Kripke-style semantics for weakening-free fuzzy logics", Korean Journal of Logic 17: pp. 181-195.
  20. Yang, E. (2014b), "Algebraic Kripke-style semantics for three-valued paraconsistent logic", Korean Journal of Logic 17: pp. 441-460.
  21. Yang, E. (2015a), "Set-theoretic Kripke-style semantics for three-valued paraconsistent logic", Korean Journal of Logic 18: pp. 65-82.
  22. Yang, E. (2015b), "Two kinds of (binary) Kripke-style semantics for three-valued logic", Logique et Analyse 231: pp. 379-396.
  23. Yang, E. (2016), "Algebraic Kripke-style semantics for an extension of HpsUL, CnHpsUL*", Korean Journal of Logic 19: pp. 107-126.