• Korean Journal of Logic
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• v.19 no.3
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• pp.437-461
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• 2016

This paper investigates weakening-free fuzzy logics with three weak forms of associativity (of multiplicative conjunction &). First, the wta-uninorm (based) logic $WA_tMUL$ 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 $WA_tMUL$ and the two axiomatic extensions with an additional axiom using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.12 no.2
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• pp.115-139
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• 2009

This paper investigates an extension of the uninorm (based) logic UL, which is obtained by adding (t-weakening, $W_t$) (($\phi$ & $\psi$) ${\wedge}$ t) $\rightarrow$ $\phi$ to UL introduced by Metcalfe and Montagna in [8]. First, the t-weakening uninorm logic $UL_{Wt}$ (the UL with $W_t$) is introduced. The algebraic structures corresponding to $UL_{Wt}$ is then defined, and its algebraic completeness is established. Next standard completeness (i.e. completeness on the real unit interval [0, 1]) is established for this logic by using Jenei and Montagna-style approach for proving standard completeness in [3, 6].