R, Fuzzy R, and Set-Theoretic Kripke-Style Semantics

R, 퍼지 R, 집합 이론적 크립키형 의미론

  • Yang, Eunsuk (Department of Philosophy & Institute of Critical Thinking and Writing, Chonbuk National University)
  • 양은석 (전북대학교 철학과, 비판적사고와논술연구소)
  • Received : 2019.03.19
  • Accepted : 2019.04.30
  • Published : 2019.06.30

Abstract

This paper deals with set-theoretic Kripke-style semantics for FR, a fuzzy version of R of Relevance. For this, first, we introduce the system FR and its corresponding Kripke-style semantics. Next, we provide set-theoretic completeness results for it.

이 글에서 우리는 연관 논리 R을 퍼지화한 체계 FR을 위한 집합 이론적인 크립키형 의미론을 다룬다. 이를 위하여 먼저 FR 체계와 그에 상응하는 크립키형 의미론을 소개한다. 다음으로 FR을 위한 집합 이론적 완전성 결과를 제공한다.

Keywords

Acknowledgement

Supported by : Chonbuk National University

References

  1. Anderson, A. R., and Belnap, N. D. (1975), Entailment: The Logic of Relevance and Necessity, vol 1, Princeton, Princeton Univ. Press.
  2. Anderson, A. R., Belnap, N. D., and Dunn, J. M. (1992), Entailment: The Logic of Relevance and Necessity, vol 2, Princeton, Princeton Univ. Press.
  3. 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
  4. Cintula, P., Horcik, R., and Noguera, C. (2015), "The quest for the basic fuzzy logic", Mathematical Fuzzy Logic, P. Hajek (Ed.), Springer Press.
  5. 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.
  6. Dunn, J. M. (1986), "Relevance logic and entailment", Handbook of Philosophical Logic, vol III, D. Gabbay and F. Guenthner (Eds.), Dordrecht, D. Reidel Publ. Co., pp. 117-224.
  7. Meyer, R. K., Dunn, J. M., and Leblanc, H. (1976), "Completeness of relevant quantification theories", Notre Dame Journal of Formal Logic 15, pp. 97-121. https://doi.org/10.1305/ndjfl/1093891202
  8. Metcalfe, G., and Montagna, F. (2007), "Substructural Fuzzy Logics", Journal of Symbolic Logic, 72, pp. 834-864. https://doi.org/10.2178/jsl/1191333844
  9. 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
  10. 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
  11. Yang, E. (2012) "R, fuzzy R, and algebraic Kripke-style semantics", Korean Journal of Logic, 15 (2), pp. 207-221. https://doi.org/10.22860/KAFL.2012.15.2.207
  12. Yang, E. (2016a) "Algebraic Kripke-style semantics for an extension of HpsUL, CnHpsUL*", Korean Journal of Logic, 19, 107-126. https://doi.org/10.22860/KAFL.2016.19.1.107
  13. Yang, E. (2016b) "Algebraic Kripke-style semantics for substructural fuzzy logics", Korean Journal of Logic 19, pp. 295-322. https://doi.org/10.22860/KAFL.2016.19.2.295
  14. Yang, E. (2017) "Set-theoretic Kripke-style semantics for involutive monoidal t-norm (based) logics", Journal of Philosophical Ideas 55(s), pp. 79-88.
  15. Yang, E. (2018a) "Set-theoretical Kripke-style semantics for an extension of HpsUL, CnHpsUL*", Korean Journal of Logic 21, pp. 39-57. https://doi.org/10.22860/KAFL.2018.21.1.39
  16. Yang, E. (2018b) "Algebraic Kripke-style semantics for weakly associative fuzzy logics", Korean Journal of Logic 21, pp. 155-173. https://doi.org/10.22860/KAFL.2018.21.2.155
  17. Yang, E. (2019) "Set-theoretic Kripke-style semantics for weakly associative fuzzy logics", Korean Journal of Logic 22, pp. 25-42. https://doi.org/10.22860/KAFL.2019.22.1.25