Many designers use the patterns of a pattern language in creating the design model. In designing with patterns, there are three aspects of the pattern language that must be taken into consideration: Structural, Syntactic, and Semantic. That means, the patterns must be applied correctly, the relationship between patterns must be correct, and the design model must be semantically correct. The syntactic aspect is important for pattern languages due to the fact that the patterns in a pattern language are interconnected via several relationships. To achieve automatic design model checking, the three aspects of a pattern language must be precisely defined. We propose formalisms for representing the Structural, Syntactic, and Semantic aspects of a pattern language. As our case study, we select a pattern language in the domain of enterprise application architecture, and show how the pattern language is described using the proposed formalism.