This paper contains an extended and improved version of the description of the FDMM formalism presented at ICEIS'2012. FDMM is a formalism to describe how meta models and models are defined in the ADOxx approach as used in the Open Models Initiative. It is based on set theory and first order logic statements. In this way, an exact description of ADOxx meta models and corresponding models can be provided. In the paper at hand we extend the description of the formalism by illustrating how the mathematical statements can be used to support the implementation on the ADOxx platform. For this purpose we show how the FDMM constructs are mapped to statements in the ADOxx Library Language (ALL). As an example of the approach, the formalism and the mapping to ALL are applied to a modeling language from the area of risk management.

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