Including semantic information in models helps to expose modeling errors early in the design process, engage a designer in a deeper understanding of the model, and standardize concepts and terminology across a development team. It is impractical, however, for model builders to manually annotate every modeling element with semantic properties. This paper demonstrates a correct, scalable and automated method to infer semantic properties using lattice-based ontologies, given relatively few manual annotations. Semantic concepts and their relationships are formalized as a lattice, and relationships within and between components are expressed as a set of constraints and acceptance criteria relative to the lattice. Our inference engine automatically infers properties wherever they are not explicitly specified. Our implementation leverages the infrastructure in the Ptolemy II type system to get efficient and scalable inference and consistency checking. We demonstrate the approach on a non-trivial Ptolemy II model of an adaptive cruise control system.