Abstract
Methods for automated classification of chemical data depend on identifying interesting parts and properties. However, classes of chemical entities which are highly symmetrical and contain large numbers of homogeneous parts (such as carbon atoms) are not straightforwardly classified in this fashion. One such class of molecules is the fullerene family, which shows potential for many novel applications including in biomedicine. The Web Ontology Language OWL cannot be used to represent the structure of fullerenes, as their structure is not tree-shaped. While individual members of the fullerene class can be modelled in standard FOL, expressing the properties of the class as a whole (independent of the count of atoms of the members) requires second-order quantification. Given the size of chemical ontologies such as ChEBI, using second-order expressivity in the general case is prohibitively expensive to practical applications. To address these conflicting requirements, we introduce a novel framework in which we heterogeneously integrate standard ontological modelling with monadic second-order reasoning over chemical graphs, enabling various kinds of information flow between the distinct representational layers.
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References
Arnborg, S.: A general purpose MSOL model checker and optimizer based on Boolean function representation. Technical report, KTH, Stockholm, Sweden (1994)
Caetano, E.W.S., Freire, V.N., dos Santos, S.G., Galvao, D.S., Sato, F.: Möbius and twisted graphene nanoribbons: stability, geometry and electronic properties. The Journal of Chemical Physics 128(164719) (2008)
Courcelle, B., Engelfriet, J.: Graph structure and monadic second-order logic—A language theoretic approach. Cambridge University Press (2011)
de Matos, P., Alcántara, R., Dekker, A., Ennis, M., Hastings, J., Haug, K., Spiteri, I., Turner, S., Steinbeck, C.: Chemical Entities of Biological Interest: an update. Nucl. Acids Res. 38, D249–D254 (2010)
Ebbinghaus, H.-D., Flum, J.: Finite Model Theory. Springer (2005)
Elsenbroich, C., Kutz, O., Sattler, U.: A Case for Abductive Reasoning over Ontologies. In: Proc. of OWLED 2006 (2006)
Canceill, J., et al.: From classical chirality to topologically chiral catenands and knots. In: Supramolecular Chemistry I Directed Synthesis and Molecular Recognition. Topics in Current Chemistry, vol. 165, pp. 131–162. Springer, Heidelberg (1993)
Wester, M.J., et al.: Scaffold Topologies. 2. Analysis of Chemical Databases. Journal of Chemical Information and Modeling 48(7), 1311–1324 (2008)
Habel, A., Pennemann, K.-H.: Correctness of high-level transformation systems relative to nested conditions. Mathematical Structures in Computer Science 19(2), 245–296 (2009)
Habel, A., Radke, H.: Expressiveness of graph conditions with variables. ECEASST 30 (2010)
Han, D., Pal, S., Liu, Y., Yan, H.: Folding and cutting DNA into reconfigurable topological nanostructures. Nature Nanotechnology 5, 712–717 (2010)
Hastings, J., Magka, D., Batchelor, C., Duan, L., Stevens, R., Ennis, M., Steinbeck, C.: Structure-based classification and ontology in chemistry. Journal of Cheminformatics 4(1), 8 (2012)
Konyk, M., De Leon, A., Dumontier, M.: Chemical Knowledge for the Semantic Web. In: Bairoch, A., Cohen-Boulakia, S., Froidevaux, C. (eds.) DILS 2008. LNCS (LNBI), vol. 5109, pp. 169–176. Springer, Heidelberg (2008)
Magka, D., Motik, B., Horrocks, I.: Modelling structured domains using description graphs and logic programming, Technical report, Dept. of Computer Science, U. of Oxford (2011)
Motik, B., Cuenca Grau, B., Horrocks, I., Sattler, U.: Representing Ontologies Using Description Logics, Description Graphs, and Rules. Artificial Intelligence 173(14), 1275–1309 (2009)
Motik, B., Sattler, U., Studer, R.: Query Answering for OWL-DL with Rules. Journal of Web Semantics: Science, Services and Agents on the World Wide Web 3(1), 41–60 (2005)
Rzepa, H.: Molecular möbius strips and trefoil knots (2003), http://www.ch.ic.ac.uk/motm/trefoil/ (last accessed December 2011)
Trinajstic, N.: Chemical graph theory. CRC Press, Florida (1992)
Tseng, H.-R., Vignon, S.A., Stoddart, J.F.: Toward chemically controlled nanoscale molecular machinery. Angewandte Chemie International Edition 42, 1491–1495 (2003)
Weisstein, E.W.: Polyhedral graph (2011), http://mathworld.wolfram.com/PolyhedralGraph.html
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Kutz, O., Hastings, J., Mossakowski, T. (2012). Modelling Highly Symmetrical Molecules: Linking Ontologies and Graphs. In: Ramsay, A., Agre, G. (eds) Artificial Intelligence: Methodology, Systems, and Applications. AIMSA 2012. Lecture Notes in Computer Science(), vol 7557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33185-5_11
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DOI: https://doi.org/10.1007/978-3-642-33185-5_11
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