Advertisement

Accessible Reasoning with Diagrams: From Cognition to Automation

  • Zohreh ShamsEmail author
  • Yuri Sato
  • Mateja Jamnik
  • Gem Stapleton
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10871)

Abstract

High-tech systems are ubiquitous and often safety and security critical: reasoning about their correctness is paramount. Thus, precise modelling and formal reasoning are necessary in order to convey knowledge unambiguously and accurately. Whilst mathematical modelling adds great rigour, it is opaque to many stakeholders which leads to errors in data handling, delays in product release, for example. This is a major motivation for the development of diagrammatic approaches to formalisation and reasoning about models of knowledge. In this paper, we present an interactive theorem prover, called iCon, for a highly expressive diagrammatic logic that is capable of modelling OWL 2 ontologies and, thus, has practical relevance. Significantly, this work is the first to design diagrammatic inference rules using insights into what humans find accessible. Specifically, we conducted an experiment about relative cognitive benefits of primitive (small step) and derived (big step) inferences, and use the results to guide the implementation of inference rules in iCon.

Notes

Acknowledgements

This research was funded by a Leverhulme Trust Research Project Grant (RPG-2016-082) for the project entitled Accessible Reasoning with Diagrams. The authors would like to thank Prof. John Howse, Dr Andrew Blake and Dr Ryo Takemura for their cooperation in the experiments.

References

  1. 1.
    Baader, F., Horrocks, I., Sattler, U.: Description logics. In: Staab, S., Studer, R. (eds.) Handbook on Ontologies, pp. 21–43. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-540-92673-3_1CrossRefGoogle Scholar
  2. 2.
    Barwise, J., Etchemendy, J.: Hyperproof. CSLI Publications, California (1994)zbMATHGoogle Scholar
  3. 3.
    Beckert, B., Grebing, S., Böhl, F.: A usability evaluation of interactive theorem provers using focus groups. In: Canal, C., Idani, A. (eds.) SEFM 2014. LNCS, vol. 8938, pp. 3–19. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-15201-1_1CrossRefGoogle Scholar
  4. 4.
    Gil, J., Howse, J., Kent, S.: Formalizing spider diagrams. In: IEEE Symposium on Visual Languages, pp. 130–137. IEEE (1999).  https://doi.org/10.1109/VL.1999.795884
  5. 5.
    Harrison, J., Urban, J., Wiedijk, F.: History of interactive theorem proving. In: Handbook of the History of Logic. Vol. 9: Computational Logic, pp. 135–214. Elsevier (2014)CrossRefGoogle Scholar
  6. 6.
    Hou, T., Chapman, P., Blake, A.: Antipattern comprehension: an empirical evaluation. In: Formal Ontology in Information Systems. Frontiers in Artificial Intelligence, vol. 283, pp. 211–224. IOS Press (2016).  https://doi.org/10.3233/978-1-61499-660-6-211
  7. 7.
    Howse, J., Stapleton, G., Flower, J., Taylor, J.: Corresponding regions in Euler diagrams. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 76–90. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-46037-3_7CrossRefGoogle Scholar
  8. 8.
    Jamnik, M.: Mathematical Reasoning with Diagrams. CSLI Publications, California (2001)zbMATHGoogle Scholar
  9. 9.
    Kortenkamp, U., Richter-Gebert, J.: Using automatic theorem proving to improve the usability of geometry software. In: Mathematical User-Interfaces Workshop (2004)Google Scholar
  10. 10.
    Linker, S., Burton, J., Blake, A.: Measuring user comprehension of inference rules in Euler diagrams. In: Jamnik, M., Uesaka, Y., Elzer Schwartz, S. (eds.) Diagrams 2016. LNCS (LNAI), vol. 9781, pp. 32–39. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-42333-3_3CrossRefGoogle Scholar
  11. 11.
    Linker, S., Burton, J., Jamnik, M.: Tactical diagrammatic reasoning. In: International Workshop on User Interfaces for Theorem Provers. Electronic Proceedings in Theoretical Computer Science, vol. 239, pp. 29–42 (2016).  https://doi.org/10.4204/EPTCS.239.3MathSciNetCrossRefGoogle Scholar
  12. 12.
    Nguyen, T.A.T., Power, R., Piwek, P., Williams, S.: Measuring the understandability of deduction rules for OWL. In: International Workshop on Debugging Ontologies and Ontology Mappings, pp. 1–12. Linköping Electronic Conference Proceedings (2012)Google Scholar
  13. 13.
    Paulson, L.C.: Isabelle - A Generic Theorem Prover (with a contribution by T. Nipkow), vol. 828. Springer, Heidelberg (1994).  https://doi.org/10.1007/BFb0030541CrossRefGoogle Scholar
  14. 14.
    Rodgers, P., Zhang, L., Purchase, H.: Wellformedness properties in Euler diagrams: which should be used? IEEE Trans. Vis. Comput. Graph. 18(7), 1089–1100 (2012).  https://doi.org/10.1109/TVCG.2011.143CrossRefGoogle Scholar
  15. 15.
    Sato, Y., Mineshima, K.: How diagrams can support syllogistic reasoning: an experimental study. J. Log. Lang. Inf. 24(4), 409–455 (2015).  https://doi.org/10.1007/s10849-015-9225-4MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Sato, Y., Ueda, K., Wajima, Y.: Strategy analysis of non-consequence inference with Euler diagrams. J. Log. Lang. Inf. 27, 61–77 (2017).  https://doi.org/10.1007/s10849-017-9259-xMathSciNetCrossRefGoogle Scholar
  17. 17.
    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_18CrossRefGoogle Scholar
  18. 18.
    Shimojima, A.: Semantic Properties of Diagrams and Their Cognitive Potentials. CSLI Publications, California (2015)Google Scholar
  19. 19.
    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).  https://doi.org/10.1109/VLHCC.2017.8103474
  20. 20.
    Stapleton, G., Howse, J., Chapman, P., Delaney, A., Burton, J., Oliver, I.: Formalizing concept diagrams. In: Visual Languages and Computing, pp. 182–187. Knowledge Systems Institute (2013)Google Scholar
  21. 21.
    Stapleton, G., Zhang, L., Howse, J., Rodgers, P.: Drawing Euler diagrams with circles: the theory of piercings. IEEE Trans. Vis. Comput. Graph. 17(7), 1020–1032 (2011).  https://doi.org/10.1109/TVCG.2010.119CrossRefGoogle Scholar
  22. 22.
    Urbas, M., Jamnik, M., Stapleton, G.: Speedith: a reasoner for spider diagrams. J. Log. Lang. Inf. 24(4), 487–540 (2015).  https://doi.org/10.1007/s10849-015-9229-0MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyUniversity of CambridgeCambridgeUK
  2. 2.Centre for Secure, Intelligent and Usable SystemsUniversity of BrightonBrightonUK

Personalised recommendations