An Arbitrary Mark is a Trademark style that has no obvious meaning to the viewer. While Product Marks symbolize the product or service that is provided the company, a Name Mark portrays a symbol that represents the company name. A Word Mark displays the organization in a stylistic manner. The Arbitrary Mark falls in none of those categories.
The most obvious example of an Arbitray Mark is that of the Nike “Swoosh”. It is a cool design without an obvious or immediately understood meaning. That is not to say that The mark has no meaning. The difference is that a meaning is generally created and assigned after the fact.