Since the seminal book by the Gang of Four, design patterns have proven an important tool in software development. Over time, more and more patterns have been discovered and developed. The sheer amount of patterns available makes it hard to find patterns useful for solving a specific design problem. Hence, tools supporting searching and finding design patterns appropriate to a certain problem are required. To develop such tooling, design patterns must be described formally such that they can be queryed by the problem to be solved. Current approaches to formalising design patterns focus on the solution structure of the pattern rather than on the problems solved. In this paper, we present a formalisation of the intent of the 23 patterns from the Gang-of-Four book. Based on this formalisation we have developed a Design Pattern Wizard that proposes applicable design patterns based on a description of a design problem.