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Relational Semantics for Fuzzy Extensions of R: Set-theoretic Approach

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This paper addresses a set-theoretic completeness based on a relational semantics for fuzzy extensions of two versions Rt and RT of R (Relevance logic). To this end, two fuzzy logics FRt and FRT as extensions of Rt and RT, respectively, and the relational semantics, so called Routley-Meyer semantics, for them are first recalled. Next, on the semantics completeness results are provided for them using a set-theoretic way.

Abstract

This paper addresses a set-theoretic completeness based on a relational semantics for fuzzy extensions of two versions Rt and RT of R (Relevance logic). To this end, two fuzzy logics FRt and FRT as extensions of Rt and RT, respectively, and the relational semantics, so called Routley-Meyer semantics, for them are first recalled. Next, on the semantics completeness results are provided for them using a set-theoretic way.

참고문헌 (14)

  1. Cintula, P., "Mathematical Fuzzy Logic" (2015), Springer Press
  2. Dunn, J. M., "Handbook of Philosophical Logic vol III", pp.117~224 (1986), D. Reidel Publ. Co
  3. Fine, K., "Models for entailment", Journal of Philosophical Logic, 3, pp.347~372 (1974)
  4. Meyer, R. K., "Completeness of relevant quantification theories", Notre Dame Journal of Formal Logic, 15, pp.97~121 (1976)
  5. Routley, R., "The semantics of entailment(II)", Journal of Philosophical Logic, 1, pp.53~73 (1972)
  6. Routley, R., "The semantics of entailment(Ⅲ)", Journal of Philosophical Logic, 1, pp.192~208 (1972)
  7. Routley, R., "Truth, Syntax, and Modality", pp.199~243 (1973), North-Holland Publ. Co
  8. 양은석, "R, fuzzy R, and Algebraic Kripke-style Semantics", 논리연구, 15(2), pp.207~221 (2012), 한국논리학회[DOI]
  9. Yang, E., "Algebraic Kripke-style semantics for relevance logics", Journal of Philosophical Logic, 43, pp.803~826 (2014)
  10. 양은석, "Routley-Meyer semantics for R", 논리연구, 18(3), pp.437~456 (2015), 한국논리학회[DOI]
  11. 양은석, "R, Fuzzy R, and Set-Theoretic Kripke-Style Semantics", 논리연구, 22(2), pp.291~307 (2019), 한국논리학회[DOI]
  12. Yang, E., "Algebraic relational semantics for basic substructural logics", Logique et Analyse, 252, pp.415~441 (2020)
  13. Yang, E., "Basic core fuzzy logics and algebraic Routley-Meyer-style semantics", Axioms, 10(4), pp.1~16 (2021)
  14. 양은석, "Fuzzy R Systems and Algebraic Routley-Meyer Semantics", 논리연구, 25(3), pp.313~332 (2022), 한국논리학회

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