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Some axiomatic extensions of the involutive mianorm Logic IMIAL

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

참고문헌 (17)

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  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. Galatos, N., "Residuated lattices: an algebraic glimpse at substructural logics" (2007), Elsevier
  7. Hájek, P., "Metamathematics of Fuzzy Logic" (1998), Kluwer
  8. Horĉík, R., "Handbook of Mathematical Fuzzy Logic, vol 1", pp.283~353 (2011), College publications
  9. Jenei, S, "A Proof of Standard completeness for Esteva and Godo's Logic MTL", Studia Logica, 70, pp.183~192 (2002)
  10. Metcalfe, G., "Substructural Fuzzy Logics", Journal of Symbolic Logic, 72, pp.834~864 (2007)
  11. 양은석, "On the Standard Completeness of an Axiomatic Extension of the Uninorm Logic", 논리연구, 12(2), pp.115~139 (2009), 한국논리학회
  12. 양은석, "MTL의 표준 완전성", 논리연구, 16(3), pp.437~452 (2013), 한국논리학회
  13. 양은석, "An Axiomatic Extension of the Uninorm Logic Revisited", 논리연구, 17(2), pp.323~348 (2014), 한국논리학회
  14. Yang, E., "Weakening-free, non-associative fuzzy logics:micanorm-based logics", Fuzzy Sets and Systems, 276, pp.43~58 (2015)
  15. Yang, E., "Basic substructural core fuzzy logics and their extensions: Mianorm-based logics", Fuzzy Sets and Systems, 301, pp.1~18 (2016)
  16. Yang, E., "Involutive basic substructural core fuzzy logics: Involutive mianorm-based logics", Fuzzy Sets and Systems, 320, pp.1~16 (2017)
  17. 양은석, "Involutive Micanorm Logics with the n-potency axiom", 논리연구, 20(2), pp.273~292 (2017), 한국논리학회

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