Illusory inferences with quantifiers

Human inference beyond syllogisms: an approach using external graphical representations

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.