Logics for finite \(\mathbf{UL}\) and \(\mathbf{IUL}\)-algebras are substructural fuzzy logics (Q2337882)

Summary: Semilinear substructural logics \(\mathbf{UL}_\omega\) and \(\mathbf{IUL}_\omega\) are logics for finite \(\mathbf{UL}\) and \(\mathbf{IUL}\)-algebras, respectively. In this paper, the standard completeness of \(\mathbf{UL}_\omega\) and \(\mathbf{IUL}_\omega\) is proven by the method developed by Jenei, Montagna, Esteva, Gispert, Godo, and Wang. This shows that \(\mathbf{UL}_\omega\) and \(\mathbf{IUL}_\omega\) are substructural fuzzy logics.