7 problems

A semilinear De Morgan monoid is a De Morgan monoid whose lattice reduct is a semilinear residuated lattice, and let $\Omega({{\sf SDMM}})$ denote the collection of varieties of se…

Finite nuclear-image conjecture. The finite nuclear images of conuclear images of negative cones of $\ell$-groups are precisely the finite integral residuated lattices.

Let $\mathsf{CIdInRL}$ denote the class of commutative idempotent involutive residuated lattices. For a member of this class, let $\langle A,\sqsubseteq\rangle$ be its associated m…

Let ${\rm {\bf HpsUL}}$ be the Hilbert system for pseudo-uninorm logic, and let ${\rm {\bf HpsUL}}^\ast$ be obtained by adding the weakly commutativity rule … Here $A$ is a formula…

The Hilbert system ${\rm {\bf HpsUL}}$ is a substructural logic associated with pseudo-uninorms and their residua. Metcalfe–Olivetti–Gabbay conjecture. The Hilbert system…

Let $A$ be a residuated lattice, let $\tilde{A}$ be its strongly co-Stone hull, and let $\epsilon:A\to\tilde{A}$ be the canonical morphism. For a subset $X\subseteq A$, write…

Quasi-local residuated lattices are being considered as a generalization of quasi-local MV-algebras and quasi-local BL-algebras, which characterize weak Boolean products of local M…