• 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].

• Korean Journal of Logic
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• v.19 no.1
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• pp.107-126
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• 2016

This paper deals with Kripke-style semantics for weakening-free non-commutative fuzzy logics. As an example, we consider an algebraic Kripke-style semantics for an extension of the pseudo-uninorm based fuzzy logic HpsUL, $CnHpsUL^*$. For this, first, we recall the system $CnHpsUL^*$, define its corresponding algebraic structures $CnHpsUL^*$-algebras, and algebraic completeness results for it. We next introduce a Kripke-style semantics for $CnHpsUL^*$, and connect it with algebraic semantics.