The logic of pseudo-uninorms and their residua (Q2335051)

Summary: Our method for density elimination is generalized to the non-commutative substructural logic \(\mathbf{GpsUL}^*\). Then, the standard completeness of \(\mathbf{HpsUL}^*\) follows as a lemma by virtue of previous work by \textit{G. Metcalfe} and \textit{F. Montagna} [J. Symb. Log. 72, No. 3, 834--864 (2007; Zbl 1139.03017)]. This result shows that \(\mathbf{HpsUL}^*\) is the logic of pseudo-uninorms and their residua and answered the question posed by \textit{G. Metcalfe} et al. [Proof theory for fuzzy logics. Dordrecht: Springer (2009; Zbl 1168.03002)] and \textit{G. Metcalfe} and \textit{C. Tsinakis} [Soft Comput. 21, No. 1, 175--189 (2017; Zbl 1396.03060)].