Abstract
This paper addresses the problem of how to visualize axioms from \(\mathcal {ALC}\) using concept diagrams. We establish that 66.4% of OWL axioms defined for ontologies in the Manchester corpus are formulated over \(\mathcal {ALC}\), demonstrating the significance of considering how to visualize this relatively simple description logic. Our solution to the problem involves providing a general translation from \(\mathcal {ALC}\) axioms into concept diagrams, which is sufficient to establish that all of \(\mathcal {ALC}\) can be expressed. However, the translation itself is not designed to give optimally readable diagrams, which is particularly challenging to achieve in the general case. As such, we also improve the translations for a selected category of \(\mathcal {ALC}\) axioms, to illustrate that more effective diagrams can be produced.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
To count axioms, we used OWL API’s DL expressiveness checker. Each axiom is extracted and provided to the OWL API which determines whether the axiom is syntactically in \(\mathcal {ALC}\). This approach is somewhat crude, in that some OWL non-\(\mathcal {ALC}\) axioms can be reduced to a set of axioms including some in \(\mathcal {ALC}\); we count such OWL axioms as not being in \(\mathcal {ALC}\). Of the ontologies in the corpus, we could parse 4019. Our counting software is an extension of an existing ontology statistics processing package [11] and can be found at https://github.com/hammar/OntoStats.
References
Manchester owl corpus. http://owl.cs.manchester.ac.uk/publications/supporting-material/owlcorpus/. Accessed Feb 2014
OntoGraf. http://protegewiki.stanford.edu/wiki/OntoGraf. Accessed July 2013
Shams, Z., Jamnik, M., Stapleton, G., Sato, Y.: Reasoning with concept diagrams about antipatterns in ontologies. In: Geuvers, H., England, M., Hasan, O., Rabe, F., Teschke, O. (eds.) CICM 2017. LNCS (LNAI), vol. 10383, pp. 255–271. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62075-6_18
Alqadah, M., Stapleton, G., Howse, J., Chapman, P.: Evaluating the impact of clutter in Euler diagrams. In: Dwyer, T., Purchase, H., Delaney, A. (eds.) Diagrams 2014. LNCS (LNAI), vol. 8578, pp. 108–122. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44043-8_15
Chapman, P., Stapleton, G., Rodgers, P., Micallef, L., Blake, A.: Visualizing sets: an empirical comparison of diagram types. In: Dwyer, T., Purchase, H., Delaney, A. (eds.) Diagrams 2014. LNCS (LNAI), vol. 8578, pp. 146–160. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44043-8_18
Compton, M., Barnaghi, P., Bermudez, L., Garcia-Castro, R., Corcho, O., Cox, S., Graybeal, J., Hauswirth, M., Henson, C., Herzog, A., Huang, V., Janowicz, K., Kelsey, W.D., Le Phuoc, D., Lefort, L., Leggieri, M., Neuhaus, H., Nikolov, A., Page, K., Passant, A., Sheth, A., Taylor, K.: The SSN ontology of the W3C semantic sensor network incubator group. Web Semant. Sci. Serv. Agents World Wide Web 17, 25–32 (2012)
Dau, F., Ekland, P.: A diagrammatic reasoning system for the description logic \(\cal{ALC}\). J. Vis. Lang. Comput. 19(5), 539–573 (2008)
Duncan, J., Humphreys, G.: Visual search and stimulus similarity. Psychol. Rev. 96, 433–458 (1989)
Flower, J., Howse, J.: Generating Euler diagrams. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 61–75. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46037-3_6
Gurr, C.: Effective diagrammatic communication: syntactic, semantic and pragmatic issues. J. Vis. Lang. Comput. 10(4), 317–342 (1999)
Hammar, K.: Reasoning performance indicators for ontology design patterns. In: 4th Workshop on Ontology and Semantic Web Patterns (2013)
Hayes, P., Eskridge, T., Mehrotra, M., Bobrovnikoff, D., Reichherzer, T., Saavedra, R.: COE: tools for collaborative ontology development and reuse. In: Knowledge Capture Conference (2005)
Horridge, M.: Owlviz. www.co-ode.org/downloads/owlviz/. Accessed June 2009
Howse, J., Stapleton, G., Taylor, K., Chapman, P.: Visualizing ontologies: a case study. In: Aroyo, L., Welty, C., Alani, H., Taylor, J., Bernstein, A., Kagal, L., Noy, N., Blomqvist, E. (eds.) ISWC 2011. LNCS, vol. 7031, pp. 257–272. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25073-6_17
John, C., Fish, A., Howse, J., Taylor, J.: Exploring the notion of ‘Clutter’ in Euler diagrams. In: Barker-Plummer, D., Cox, R., Swoboda, N. (eds.) Diagrams 2006. LNCS (LNAI), vol. 4045, pp. 267–282. Springer, Heidelberg (2006). https://doi.org/10.1007/11783183_36
Riche, N., Dwyer, T.: Untangling Euler diagrams. IEEE Trans. Visual Comput. Graphics 16(6), 1090–1099 (2010)
Shams, Z., Jamnik, M., Stapleton, G., Sato, Y.: Reasoning with concept diagrams about antipatterns. In: 21st International Conference on Logic for Programming, Artificial Intelligence, and Reasoning. pp. 27–42. Kapla Publications in Computing (2017)
Shams, Z., Jamnik, M., Stapleton, G., Sato, Y.: Reasoning with concept diagrams about antipatterns in ontologies. In: Geuvers, H., England, M., Hasan, O., Rabe, F., Teschke, O. (eds.) CICM 2017. LNCS (LNAI), vol. 10383, pp. 255–271. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62075-6_18
Shams, Z., Sato, Y., Jamnik, M., Stapleton, G.: Accessible reasoning with diagrams: from cognition to automation. In: 10th International Conference on the Theory and Application of Diagrams. LNCS, vol. 10871. Springer (2018)
Simonetto, P., Auber, D., Archambault, D.: Fully automatic visualisation of overlapping sets. Comput. Graphics Forum 28(3), 967–974 (2009)
Stapleton, G., Compton, M., Howse, J.: Visualizing OWL 2 using diagrams. In: IEEE Symposium on Visual Languages and Human-Centric Computing, pp. 245–253. IEEE (2017)
Stapleton, G., Flower, J., Rodgers, P., Howse, J.: Automatically drawing Euler diagrams with circles. J. Vis. Lang. Comput. 23, 163–193 (2012)
Stapleton, G., Howse, J., Chapman, P., Delaney, A., Burton, J., Oliver, I.: Formalizing concept diagrams. In: 19th International Conference on Distributed Multimedia Systems, pp. 182–187. KSI (2013)
Acknowledgement
Gem Stapleton was partially funded by a Leverhulme Trust Research Project Grant (RPG-2016-082) for the project entitled Accessible Reasoning with Diagrams.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Stapleton, G., Delaney, A., Compton, M., Chapman, P. (2018). Visualizing \(\mathcal {ALC}\) Using Concept Diagrams. In: Croitoru, M., Marquis, P., Rudolph, S., Stapleton, G. (eds) Graph Structures for Knowledge Representation and Reasoning. GKR 2017. Lecture Notes in Computer Science(), vol 10775. Springer, Cham. https://doi.org/10.1007/978-3-319-78102-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-78102-0_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78101-3
Online ISBN: 978-3-319-78102-0
eBook Packages: Computer ScienceComputer Science (R0)