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This article surveys the use of logic in computational models of legal reasoning, against the background of a four-layered view on legal argument. This view comprises a logical layer (constructing an argument); a dialectical layer (comparing and assessing conflicting arguments); a procedural layer (regulating the process of argumentation); and a strategic, or heuristic layer (arguing persuasively). Each further layer presupposes, and is built around the previous layers. At the first two layers the information base is fixed, while at the third and fourth layer it is constructed dynamically, during a dialogue or dispute.