The formal specification of design patterns is widely recognised as being vital to their effective and correct use in software development. It can clarify the concepts underlying patterns, eliminate ambiguity and thereby lay a solid foundation for tool support. This paper further advances an approach that uses first order predicate logic to specify design patterns by capturing the dynamic behaviour represented in sequence diagrams. A case study of all 23 patterns in the Gang of Four catalogue demonstrates that it can not only capture dynamic features but also simplify the specification of structural properties.