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Fuzzy R Systems and Algebraic Routley-Meyer Semantics

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Here algebraic Routley-Meyer semantics is addressed for two fuzzy versions of the logic of relevant implication R. To this end, two versions Rt and RT of R and their fuzzy extensions FRt and FRT, respectively, are first discussed together with their algebraic semantics. Next algebraic Routley-Meyer semantics for these two fuzzy extensions is introduced. Finally, it is verified that these logics are sound and complete over the semantics.

Abstract

Here algebraic Routley-Meyer semantics is addressed for two fuzzy versions of the logic of relevant implication R. To this end, two versions Rt and RT of R and their fuzzy extensions FRt and FRT, respectively, are first discussed together with their algebraic semantics. Next algebraic Routley-Meyer semantics for these two fuzzy extensions is introduced. Finally, it is verified that these logics are sound and complete over the semantics.

참고문헌 (19)

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  11. 양은석, "Uninorm logic: toward a fuzzy-relevance logic(2)", 논리연구, 11(1), pp.131~156 (2008), 한국논리학회
  12. 양은석, "Non-associative fuzzy-relevance logics: strong t-associative monoidal uninorm logics", 논리연구, 12(1), pp.89~110 (2009), 한국논리학회
  13. 양은석, "R, fuzzy R, and Algebraic Kripke-style Semantics", 논리연구, 15(2), pp.207~221 (2012), 한국논리학회[DOI]
  14. Yang, E., "R and Relevance principle revisited", Journal of Philosophical Logic, 42, pp.767~782 (2013)
  15. 양은석, "Routley-Meyer semantics for R", 논리연구, 18(3), pp.437~456 (2015), 한국논리학회[DOI]
  16. Yang, E, "Substructural fuzzy-relevance logic", Notre Dame Journal of Formal Logic, 56, pp.471~491 (2015)
  17. 양은석, "R, Fuzzy R, and Set-Theoretic Kripke-Style Semantics", 논리연구, 22(2), pp.291~307 (2019), 한국논리학회[DOI]
  18. Yang, E., "Algebraic relational semantics for basic substructural logics", Logique et Analyse, 252, pp.415~441 (2020)
  19. Yang, E., "Basic core fuzzy logics and algebraic Routley-Meyer-style semantics", Axioms, 10(4), pp.273~ (2021)

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