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Performing computational experiments on mathematical models instead of building and testing physical prototypes can drastically reduce the develop cost for complex systems such as automobiles, aircraft, and powerplants. In the past three decades, a new category of equation-based modeling languages has appeared that is based on acausal and objectoriented modeling principles, enabling good reuse of models. However, the modeling languages within this category have grown to be large and complex, where the specifications of the language’s semantics are informally defined, typically described in natural languages. The lack of a formal semantics makes these languages hard to interpret unambiguously and to reason about. This thesis concerns the problem of designing the semantics of such equation-based modeling languages in a way that allows formal reasoning and increased correctness. The work is presented in two parts. In the first part we study the state-of-the-art modeling language Modelica. We analyze the concepts of types in Modelica and conclude that there are two kinds of type concepts: class types and object types. Moreover, a concept called structural constraint delta is proposed, which is used for isolating the faults of an over-or under-determined model. In the second part, we introduce a new research language called the Modeling Kernel Language (MKL). By introducing the concept of higher-order acausal models (HOAMs), we show that it is possible to create expressive modeling libraries in a manner analogous to Modelica, but using a small and simple language concept. In contrast to the current state-of-the-art …