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This paper discusses ontologies, methods for developing them and languages for representing them. A special ontology for computational support of the Conceptual ReDesign Process (CRDP) is introduced with a simple illustrative example of an application. The ontology denoted as Global context (GLB) combines features of general semantic networks and features of UML language. The ontology is task-oriented and domain-oriented, and contains three basic strata – GLB Expl (stratum of Explanation), GLB FAct (stratum of Fields of Activities) and GLB Env (stratum of Environment), with their sub-strata. The ontology has been developed to represent functions of systems and their components in CRDP. The main difference between this ontology and ontologies which have been developed to identify functions (the semantic details in those ontologies must be as deep as possible) is in the style of the description of the functions. In the proposed ontology, Formation Spaces were used as lower semantic categories the semantic deepness of which is variable and depends on the actual solution approach of a specialised Conceptual Designer.

Ontologies and Formation Spaces for Conceptual ReDesign of Systems