Human inference beyond syllogisms: an approach using external graphical representations

  • Yuri SatoEmail author
  • Gem Stapleton
  • Mateja Jamnik
  • Zohreh Shams
Research Article


Research in psychology about reasoning has often been restricted to relatively inexpressive statements involving quantifiers (e.g. syllogisms). This is limited to situations that typically do not arise in practical settings, like ontology engineering. In order to provide an analysis of inference, we focus on reasoning tasks presented in external graphic representations where statements correspond to those involving multiple quantifiers and unary and binary relations. Our experiment measured participants’ performance when reasoning with two notations. The first notation used topological constraints to convey information via node-link diagrams (i.e. graphs). The second used topological and spatial constraints to convey information (Euler diagrams with additional graph-like syntax). We found that topo-spatial representations were more effective for inferences than topological representations alone. Reasoning with statements involving multiple quantifiers was harder than reasoning with single quantifiers in topological representations, but not in topo-spatial representations. These findings are compared to those in sentential reasoning tasks.


Inference Diagrammatic reasoning External representation Quantifiers Binary predicates 



Parts of this study were presented in the 40th CogSci Conference (July, 2018) in Madison. The authors would like to thank John Howse, Andrew Blake and Ryo Takemura for cooperating on the experiments.


This research was funded by a Leverhulme Trust Research Project Grant (RPG-2016-082) for the project entitled Accessible Reasoning with Diagrams.

Compliance with ethical standards

Conflict of interest

The authors have no conflict of interest to declare.

Ethical approval

All procedures performed in the experiment involving human participants were in accordance with the ethical standards of the institutional and national research committee and with the 1964 Declaration of Helsinki and its later amendments.

Informed consent

Informed consent was obtained from all individual participants included in the experiment.

Supplementary material (7.2 mb)
Appendix: Materials and instructions used in the experiment (zip 7379 KB)


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Copyright information

© Marta Olivetti Belardinelli and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

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

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