How to model the shapes of molecules? Combining topology and ontology using heterogeneous specifications

Classification of chemical entities is generally based on identifying the interesting parts and properties of the molecules. However, classes of chemical entities which are highly symmetrical and which contain large numbers of homogeneous parts (such as carbon atoms) are not straightforwardly classified in this fashion. One such class of molecules is the recently developed fullerene family, discovery of which led to the award of the Nobel prize for chemistry in 1996. Fullerene molecules show potential for many novel applications including in biomedicine. Whilst standard knowledge representation approaches in chemistry are inadequate to allow the automatic classification of chemical entities as members of the fullerene class based on their chemical structure, standard OWL representations are insufficient for this task as well. We here sketch an alternative framework in which we heterogeneously integrate ontological modelling with monadic second-order reasoning over chemical graphs and topological features of the molecules, enabling a threefold information flow between these distinct representational layers, namely a debugging of the ontology, an abductive enrichment of the ontology, and an inductive learning of new graph classes.