The formalization mechanism in this work uses algebraic specifications as a high-level formal language to derive a formal model from the conceptual model. The theory behind algebraic specifications has been developed and used in software design. There are only few applications to generic geometric problems. This project is ongoing research and there are no final results yet. The ontology has been defined for both flat and hierarchical case.
Hierarchical structure is imposed on space to allow efficient spatial reasoning.
The formalization is partly done. Another, more general case of hierarchical structurization of space to look closer at, is Christaller's space. A hierarchical structure, which is the same on each level, uses boundaries that do not exist in nature. Formalization of underlying, already existing Christaller's model according to the posited general principles of hierarchical spatial reasoning would be another suitable case study.