? 2022 Elsevier B.V.This paper presents the multi-adjoint lattice logic (MLL) and its completeness and soundness. Specifically, the proposed many-valued propositional logic framework is defined on a multi-adjoint algebra whose underlying algebraic structure is a bounded lattice, which embeds the well-known basic logic (BL) given by Hájek on residuated lattices. The consideration of truth-stressing hedges in the multi-adjoint algebra is also studied and, as a consequence, two new logics extensions of MLL arise: the multi-adjoint lattice logic very true intensified (MLLvt) and the multi-adjoint lattice logic ∨-very true intensified (MLL∨?vt). Finally, the soundness and completeness of the aforementioned logics are also proven.
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