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This paper investigates weakening-free fuzzy logics with three weak forms of associativity (of multiplicative conjunction &). First, the wta-uninorm (based) logic WAtMUL and its two axiomatic extensions are introduced as weakening-free weakly associative fuzzy logics. The algebraic structures corresponding to the systems are then defined, and algebraic completeness results for them are provided. Next, standard completeness is established for WAtMUL and the two axiomatic extensions with an additional axiom using construction in the style of Jenei-Montagna.
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참고문헌 (16)
참고문헌 신청
Cintula, P. / 2006 / Weakly Implicative(Fuzzy)Logics I : Basic properties / Archive for Mathematical Logic 45:673~704
Cintula, P. / 2013 / Non-associative substructural logics and their semilinear extensions : axiomatization and completeness properties / Review of Symbol. Logic 12:394~423
Cintula, P. / 2015 / Mathematical Fuzzy Logic / Springer
Cintula, P. / 2011 / Handbook of Mathematical Fuzzy Logic, vol 1 / College publications :103~207
Esteva, F. / 2002 / On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm logic / Studia Logica 71:393~420
Cintula, P. / 2013 / Non-associative substructural logics and their semilinear extensions : axiomatization and completeness properties / Review of Symbol. Logic 12:394~423
Cintula, P. / 2015 / Mathematical Fuzzy Logic / Springer
Cintula, P. / 2011 / Handbook of Mathematical Fuzzy Logic, vol 1 / College publications :103~207
Esteva, F. / 2002 / On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm logic / Studia Logica 71:393~420
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