Measurement theoretic representation of large, diverse model bases: The unified modeling language LU

摘要

The philosophy and features of the Unified Modeling Language LU are presented with emphasis on the support of large, diverse model bases. We argue that measurement theory stressing homomorphic mappings from empirical to mathematical systems is an ideal foundation for integrated modeling environments. Homomorphic mappings are an integral part of the semantics of the LU and motivate a number of language features that support large, diverse model bases. The LU provides a separate but uniform representation of domain worlds and mathematical systems known as model types. Domain worlds are composed of empirical objects, relations, and functions organized into classes and attributes, while model types are defined by standard queries and a rich collection of assumptions. To emphasize the importance of homomorphic mappings, unification constraints combine common patterns of domain and mathematical knowledge in model templates. Reusability and incremental refinement are supported by inheritance based on partial order relations for classes, attributes, assumptions, and model types. Together, the semantic foundation and language features provide a practical and formal knowledge representation for large, diverse model bases.