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Micanorm-Based Logics with Fixed-Point

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Standard completeness for fixed-pointed mianorm-based logics were recently introduced by Yang. Here, we extend it to logics with commutativity, i.e., fixed-pointed micanorm-based logics. More precisely, some fixed-pointed micanorm-based logics and their algebraic semantics are first discussed. Next, several examples of fixed-pointed micanorms are introduced. Standard completeness results are finally provided for those logics.

Abstract

Standard completeness for fixed-pointed mianorm-based logics were recently introduced by Yang. Here, we extend it to logics with commutativity, i.e., fixed-pointed micanorm-based logics. More precisely, some fixed-pointed micanorm-based logics and their algebraic semantics are first discussed. Next, several examples of fixed-pointed micanorms are introduced. Standard completeness results are finally provided for those logics.

참고문헌 (13)

  1. Baldi, P., "A note on standard completeness for some extensions of uninorm logic", Soft Computing, 18, pp.1463~1470 (2014)
  2. Baldi, P, "Standard completeness for uninorm-based logics", IEEE International Symposium on Multiple-Valued Logic, IEEE, pp.78~83 (2015)
  3. Běhounek, L., "Fuzzy logics as the logics of chains", Fuzzy Sets and Systems, 157, pp.604~610 (2006)
  4. Cintula, P., "Non-associative substructural logics and their semilinear extensions : axiomatization and completeness properties", Review of Symbol. Logic, 12, pp.394~423 (2013)
  5. Cintula, P., "Mathematical Fuzzy Logip" (2015), Springer
  6. Cintula, P., "A general framework for mathematical fuzzy logic, Handbook of Mathematical Fuzzy Logic, vol 1", pp.103~207 (2011), College publications
  7. Horĉík, R., "Algebraic semantics: semilinear FL-algebras, Handbook of Mathematical Fuzzy Logic, vol 1", pp.283~353 (2011), College publications
  8. Yang, E., "Weakening-free, non-associative fuzzy logics : Micanorm-based logics", Fuzzy Sets and Systems, 276, pp.43~58 (2015)
  9. Yang, E., "Basic substructural core fuzzy logics and their extensions : Mianorm-based logics", Fuzzy Sets and Systems, 301, pp.1~18 (2016)
  10. Yang, E., "Mianorm-based logics with n-contraction and n-mingle axioms", Journal of Intelligent and Fuzzy systems, 37, pp.7895~7907 (2019)
  11. 양은석, "Mianorm-based Logics with right and left n-potency axioms", 논리연구, 23(1), pp.1~23 (2020), 한국논리학회[DOI]
  12. 양은석, "Fixpointed Mianorm-Based Logics", 한국지능시스템학회 논문지, 30(5), pp.360~365 (2020), 한국지능시스템학회
  13. 양은석, "Involutive extensions of fixpointed mianorm-based logics", 논리연구, 24(1), pp.31~52 (2021), 한국논리학회

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