Abstract
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.
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Notes
Middle terms appear in both major premises (containing major terms) and minor premises (containing minor terms), and minor and major terms compose conclusions.
In addition, Stenning and van Lambalgen clearly stated that “If the interpretation is not fixed, what is one actually testing? (p. 291)”.
As discussed in Stenning (2002, Chap. 2), graph (node-link) representations can essentially be the same as sentential representations with respect to expressivity.
https://protegewiki.stanford.edu/wiki/SOVA (Accessed Dec. 2017)
In the paper, each class (concept) may denote an empty or non-empty set. Consequently, each minimal region (i.e. a region having no other region contained within it) in a concept diagram also may denote an empty or a non-empty set. Thus, when the relation between two curves is unknown, they are represented as two partially overlapping curves. Note that full understanding of diagrammatic semantics with respect to partially overlapping curves is not required for understanding the cognitive strategy described here. If people find that an inclusion or exclusion relationship is unspecified to be merged, they can judge the validities of arguments. Indeed, in Sato et al. (2018b) who recorded the coordinate values of diagrams as they were moved by reasoners, it was reported that some reasoners really enumerated multiple possible configurations of inclusion, exclusion, and overlapping relationships, instead of placing curves as partially overlapping.
This kind of difficulty in premise integration can also arise in reasoning with Euler diagrams in cases of syllogisms having an existential premise (e.g. All B are A; some C are B. Therefore, some C are A); see Sato and Mineshima (2015).
In statistical hypothesis testing, the null hypotheses corresponding to the above predictions are that there is no significant difference between the two conditions. While the predictions of (2), (3), and (5) indicate that the null hypotheses are expected to be rejected, the predictions of (1) and (4) indicate that the null hypotheses are not expected to be rejected. Of course, there is no rigorous method of validating that no statistically significant difference (effect) exists. However, should we find no significant difference then this, at the very least, supports our predictions (1) and (4) and, thus, allows us to discuss the nature of human inference in question here.
This is consistent with the view that diagrammatic reasoning is a kind of surrogated reasoning (Barwise and Shimojima 1995), in which reasoning about statements having semantic values is partially taken over by operations on external aids such as diagrams (for various examples of diagrammatic reasoning, see Glasgow et al. 1995). Notions related to surrogation have also been discussed as analogical mapping in Gentner et al. (2001), Funt (1980), Steels (1990), and Chandrasekaran (2011).
For example, errors caused by the misinterpretation of premises should be prevented here, as discussed in the Introduction.
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Acknowledgements
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.
Funding
This research was funded by a Leverhulme Trust Research Project Grant (RPG-2016-082) for the project entitled Accessible Reasoning with Diagrams.
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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.
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Sato, Y., Stapleton, G., Jamnik, M. et al. Human inference beyond syllogisms: an approach using external graphical representations. Cogn Process 20, 103–115 (2019). https://doi.org/10.1007/s10339-018-0877-2
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DOI: https://doi.org/10.1007/s10339-018-0877-2