본문 바로가기
KERD
논문KCI 등재

Algebraic Kripke-style semantics for substructural fuzzy logics

1

조회

0

다운로드

10

인용

0

참고문헌

키워드

주제분류철학

초록

This paper deals with Kripke-style semantics, which will be called algebraic Kripke-style semantics, for fuzzy logics based on uninorms (so called uninorm-based logics). First, we recall algebraic semantics for uninorm-based logics. In the general framework of uninorm-based logics, we next introduce various types of general algebraic Kripke-style semantics, and connect them with algebraic semantics. Finally, we analogously consider particular algebraic Kripke-style semantics, and also connect them with algebraic semantics.

Abstract

This paper deals with Kripke-style semantics, which will be called algebraic Kripke-style semantics, for fuzzy logics based on uninorms (so called uninorm-based logics). First, we recall algebraic semantics for uninorm-based logics. In the general framework of uninorm-based logics, we next introduce various types of general algebraic Kripke-style semantics, and connect them with algebraic semantics. Finally, we analogously consider particular algebraic Kripke-style semantics, and also connect them with algebraic semantics.

참고문헌 (32)

  1. Bimbo, K., "Four-valued logic", Notre Dame Journal of Formal Logic, 42, pp.171~192 (2002)
  2. Blok, W. J., "Algebraizable Logic" (1989), American Methematical Society
  3. Ciabattoni, A., "T-norm-based logics with n-contraction", Special Issue on SOFSEM2002of Neural Network World, 12, pp.453~460 (2002)
  4. Cintula, P., "Weakly Implicative(Fuzzy)Logics I : Basic properties", Archive for Mathematical Logic, 45, pp.673~704 (2006)
  5. Cintula, P., "Distinguished algebraic semantics for t-norm-based Fuzzy Logics", Annals of Pure and Applied Logic, 160, pp.53~81 (2009)
  6. Cintula, P., "Handbook of Mathematical Fuzzy Logic, vol 1", pp.103~207 (2011), College publications
  7. Diaconescu, D., "On the forcing semantics for monoidal t-norm based logic", Journal of Universal Computer Science, 13, pp.1550~1572 (2007)
  8. Dunn, J. M., "A Kripke-style semantics for R-Mingle using a binary accessibility relation", Studia Logica, 35, pp.163~172 (1976)
  9. Dunn, J. M., "Partiality and its Dual", Studia Logica, 66, pp.5~40 (2000)
  10. Gabbay, D., "Fuzzy Logics based on [0, 1)-continuous uninorms", Archive for Mathematical Logic, 46, pp.425~449 (2007)
  11. Kripke, S., "Semantic analysis of modal logic I: normal modal propositional calculi", Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 9, pp.67~96 (1963)
  12. Kripke, S., "Formal systems and Recursive Functions", pp.92~129 (1965), North-Holland Publ Co
  13. Kripke, S., "The theory of models", pp.206~220 (1965), North-Holland Publ Co
  14. Metcalfe, G., "Substructural Fuzzy Logics", Journal of Symbolic Logic, 72, pp.834~864 (2007)
  15. Metcalfe, G., "Proof Theory for Fuzzy Logics" (2009), Springer
  16. Montagna, F., "On weakly cancellative fuzzy logics", Journal of Logic and Computation, 16, pp.423~450 (2006)
  17. Montagna, F., "Kripke semantics, undecidability and standard completeness for Esteva and Godo's Logic MTL∀", Studia Logica, 71, pp.227~245 (2002)
  18. Montagna, F., "Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 49, pp.629~641 (2003)
  19. Montagna, F., "Corrigendum to"Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 50, pp.104~107 (2004)
  20. Novak, V., "On the syntactico-semantical completeness of first-order fuzzy logic I, II", Kybernetika, 26, pp.47~66 (1990)
  21. Thomason, R. H., "A semantic study of constructive falsity", Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 15, pp.247~257 (1969)
  22. Tsinakis, C., "The structure of residuated lattices", International Journal of Algebra and Computation, 13, pp.437~461 (2003)
  23. Urquhart, A., "Handbook of Philosophical Logic, vol. 3", pp.71~116 (1986), Reidel Publ Co
  24. Wang, S., "A fuzzy logic for an ordinal sum t-norm", Fuzzy Sets and Systems, 149, pp.297~307 (2005)
  25. Wang, S., "NMŁ, a schematic extension of F. Esteva and L. Godo's logic MTL", Fuzzy Sets and Systems, 149, pp.285~295 (2005)
  26. Yager, R. R., "Uninorm aggregation operators", Fuzzy Sets and Systems, 80, pp.111~120 (1996)
  27. Yang, E., "(Star-based)four-valued Kripke-style Semantics for some neighbors of E, R, T", Logique et Analyse, 207, pp.255~280 (2009)
  28. Yang, E., "(Star-based)three-valued Kripke-style semantics for pseudo-and weak-Boolean logics", Logic Journal of the IGPL, 20, pp.187~206 (2012)
  29. 양은석, "Kripke-style Semantics for UL", 논리연구, 15(1), pp.1~15 (2012), 한국논리학회
  30. Yang, E., "Algebraic Kripke-Style Semantics for Relevance Logics", Journal of Philosophical Logic, 43, pp.803~826 (2014)
  31. 양은석, "Algebraic Kripke-style semantics for weakening-free fuzzy logics", 논리연구, 17(1), pp.181~195 (2014), 한국논리학회
  32. Eunsuk Yang, "Basic substructural core fuzzy logics and their extensions: Mianorm-based logics", Fuzzy Sets and Systems, 301, pp.1~18 (2016), Elsevier BV[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (4건)