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

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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.

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.

참고문헌 (17)

  1. Anderson, A. R., "Entailment: The Logic of Relevance and Necessity, vol 1" (1975), Princeton Univ. Press
  2. Anderson, A. R., "Entailment: The Logic of Relevance and Necessity, vol 2" (1992), Princeton Univ. Press
  3. Cintula, P., "Weakly Implicative (Fuzzy) Logics I: Basic properties", Archive for Mathematical Logic, 45, pp.673~704 (2006)
  4. Cintula, P., "Mathematical Fuzzy Logic" (2015), Springer Press
  5. Cintula, P, "A general framework for mathematical fuzzy logic, Handbook of Mathematical Fuzzy Logic, vol 1", pp.103~207 (2011), College publications
  6. Dunn, J. M., "Handbook of Philosophical Logic, vol III", pp.117~224 (1986), Reidel Publ. Co
  7. Meyer, R. K., "Completeness of relevant quantification theories", Notre Dame Journal of Formal Logic, 15, pp.97~121 (1976)
  8. Metcalfe, G., "Substructural Fuzzy Logics", Journal of Symbolic Logic, 72, pp.834~864 (2007)
  9. Montagna, F, "Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 49, pp.629~641 (2003)
  10. Montagna, F, "Corrigendum to “Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 50, pp.104~107 (2004)
  11. 양은석, "R, fuzzy R, and Algebraic Kripke-style Semantics", 논리연구, 15(2), pp.207~221 (2012), 한국논리학회[DOI]
  12. 양은석, "Algebraic Kripke-style Semantics for an Extension of HpsUL, CnHpsUL", 논리연구, 19(1), pp.107~126 (2016), 한국논리학회[DOI]
  13. 양은석, "Algebraic Kripke-style semantics for substructural fuzzy logics", 논리연구, 19(2), pp.295~322 (2016), 한국논리학회[DOI]
  14. 양은석, "Set-theoretic Kripke-style Semantics for Involutive Monoidal T-norm (Based) Logics", 철학사상, pp.79~88 (2017), 철학사상연구소[DOI]
  15. 양은석, "Set-Theoretical Kripke-Style Semantics for an Extension of HpsUL, CnHpsUL", 논리연구, 21(1), pp.39~57 (2018), 한국논리학회[DOI]
  16. 양은석, "Algebraic Kripke-Style Semantics for Weakly Associative Fuzzy Logics", 논리연구, 21(2), pp.155~173 (2018), 한국논리학회[DOI]
  17. 양은석, "Set-theoretic Kripke-style Semantics for Weakly Associative Substructural Fuzzy Logics", 논리연구, 22(1), pp.25~42 (2019), 한국논리학회[DOI]

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