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Some Axiomatic Extensions of the Involutive Micanorm Logic IMICAL

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In this paper, we deal with standard completeness of some axiomatic extensions of the involutive micanorm logic IMICAL. More precisely, first, four involutive micanorm-based logics are introduced. Their algebraic structures are then defined, and their corresponding algebraic completeness is established. Next, standard completeness is established for two of them using construction in the style of Jenei-Montagna.

Abstract

In this paper, we deal with standard completeness of some axiomatic extensions of the involutive micanorm logic IMICAL. More precisely, first, four involutive micanorm-based logics are introduced. Their algebraic structures are then defined, and their corresponding algebraic completeness is established. Next, standard completeness is established for two of them using construction in the style of Jenei-Montagna.

참고문헌 (13)

  1. Cintula, P., "Weakly Implicative (Fuzzy) Logics I: Basic properties", Archive for Mathematical Logic, 45, pp.673~704 (2006)
  2. Cintula, P., "Non-associative substructural logics and their semilinear extensions: axiomatization and completeness properties", Review of Symbolic Logic, 12, pp.394~423 (2013)
  3. Cintula, P., "Mathematical Fuzzy Logic", pp.245~290 (2015), Springer
  4. Cintula, P., "Handbook of Mathematical Fuzzy Logic, vol 1", pp.103~207 (2011), College publications
  5. Esteva, F., "On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm logic", Studia Logica, 71, pp.393~420 (2002)
  6. Hájek, P., "Metamathematics of Fuzzy Logic" (1998), Kluwer
  7. Horĉík, R., "Handbook of Mathematical Fuzzy Logic, vol 1", pp.283~353 (2011), College publications
  8. Jenei, S., "A Proof of Standard completeness for Esteva and Godo's Logic MTL", Studia Logica, 70, pp.183~192 (2002)
  9. Metcalfe, G., "Substructural Fuzzy Logics", Journal of Symbolic Logic, 72, pp.834~864 (2007)
  10. 양은석, "On the Standard Completeness of an Axiomatic Extension of the Uninorm Logic", 논리연구, 12(2), pp.115~139 (2009), 한국논리학회
  11. 양은석, "MTL의 표준 완전성", 논리연구, 16(3), pp.437~452 (2013), 한국논리학회
  12. 양은석, "An Axiomatic Extension of the Uninorm Logic Revisited", 논리연구, 17(2), pp.323~348 (2014), 한국논리학회
  13. Yang, E., "Weakening-free, non-associative fuzzy logics: Micanorm-based logics", Fuzzy Sets and Systems, 276, pp.43~58 (2015)

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