Spatial conditionals and illusory inferences

ABSTRACT

Studies of reasoning often concern specialised domains such as conditional inferences or transitive inferences, but descriptions often cut across such domains, for example:

If the circle is to the left of the square then the triangle is to the right of the square.

The square is to the right of the circle.

The triangle is to the right of the square.

Could all three of these assertions be true at the same time?

We report four experiments testing the mental model theory of such problems, which combine spatial transitivity and conditional relations. It predicts that reasoners should try to find a single mental model in which all the assertion hold:

○ □ ∆

Such problems should be easier than those that call for a model in which both clauses of the conditional are false, as when the conditional above occurs with:

The square is to the left of the circle.

The triangle is to the left of the square.

In this case, most participants had the “illusion” that the set was inconsistent (Experiment 1). Analogous results occurred when participants evaluated whether a diagram, such as the one above, depicted a possible spatial arrangement (Experiment 2), and when they evaluated the consistency of a conditional and a conjunction (Experiment 3), and of sets of assertions that contained two conditionals (Experiment 4). The findings appear to be beyond the explanatory scope of theories of reasoning based on logical rules or on probabilities.

KEYWORDS:

• Consistency
• conditional reasoning
• deduction
• mental models
• relational reasoning
• spatial reasoning

Acknowledgements

The authors are grateful to Sangeet Khemlani and Max Lotstein for their help, advice, and criticisms of a previous version of the paper. The authors thank three anonymous reviewers for stimulating criticisms.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) with a Heisenberg-grant to the first author RA 1934/3-1 and the project R8-[CSPACE] as part of the Transregional Collaborative Research Center SFB/TR 8 Spatial Cognition and in part by a grant to the third author from the National Science Foundation SES 0844851 to study deductive and probabilistic reasoning.