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In this paper, two types of gradational L-type lattice-valued propositional logic L v p l with truth values in a lattice implication algebra are introduced and some fundamental questions of them such as semantics, syntax and compactness are investigated, and where the L-type α-Soundness Theorem, (α, β)-Completeness Theorem, (α, β)-Consistent Theorem and (α, β, θ)-Deduction Theorem are also proved.