Spatial conditionals and illusory inferences

Abstract

ABSTRACTStudies 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.