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R, fuzzy R, and Algebraic Kripke-style Semantics

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This paper deals with Kripke-style semantics for FR, a fuzzy version of R of Relevance. For this, first, we introduce FR, define the corresponding algebraic structures FR-algebras, and give algebraic completeness results for it. We next introduce an algebraic Kripke-style semantics for FR, and connect it with algebraic semantics. We furthermore show that such semantics does not work for R.

Abstract

This paper deals with Kripke-style semantics for FR, a fuzzy version of R of Relevance. For this, first, we introduce FR, define the corresponding algebraic structures FR-algebras, and give algebraic completeness results for it. We next introduce an algebraic Kripke-style semantics for FR, and connect it with algebraic semantics. We furthermore show that such semantics does not work for R.

참고문헌 (12)

  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", pp.673~704 (2006), Archive for Mathematical Logic
  4. Dunn, J. M., "A Kripke-style semantics for R-Mingle using a binary accessibility relation", Studia Logica, 35, pp.163~172 (1976)
  5. Dunn, J. M., "Relevance logic and entailment5", pp.117~224 (1986), Reidel Publ. Co
  6. Dunn, J. M., "Partiality and its Dual", Studia Logica, 66, pp.5~40 (2000)
  7. Meyer, R. K., "Completeness of relevant quantification theories", NotreDame Journal of Formal Logic, 15, pp.97~121 (1976)
  8. Montagna, F, "Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 49, pp.629~641 (2003)
  9. Montagna, F, "Corrigendum to“Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 50, pp.104~107 (2004)
  10. Tsinakis, C., "The structure of residuated lattices", International Journal of Algebra and Computation, 13, pp.437~461 (2003)
  11. 양은석, "Kripke-style Semantics for UL", 논리연구, 15(1), pp.1~15 (2012), 한국논리학회
  12. Yang, E, "Algebraic Kripke-style semantics for relevance logics", manuscript, ~

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