According to the BJCP, the denomination "Quadruple/Quadrupel" is within the Belgian Dark Strong Ale style, due to its similarity in sensory aspects (strength and color). In addition, in the history of the brewing world, they became the nomenclature for consumers to understand that this beer would be a stronger version in alcohol according to this progressive sequence: Enkel/Singel, Dubbel, Tripel and Quadrupel.
In general, they are beers with a color between intense amber to a dark coppery brown, complex malt aromas, sweet profile, flavor similar to aroma. They are characterized by a high carbonic level that is not sharp, there is a clearly perceptible presence of alcoholic warmth, the sensation of body usually oscillates between medium and intense, full and creamy.
*Source: Beer Judge Certification Program (BJCP) - Beer Style Guidelines