Preferences and illusions in quantified spatial relational reasoning

Abstract

The following presents the results of an investigation of strategies and preferences in human reasoning about quantified spatial relational assertions. An empirical study revealed a clear preference effect for specific models: The initially constructed model depends on the number of mental model operations. The participants' strategies can be classified as follows: (1) Models with grouped elements are preferred; (2) Models are constructed according to a parsimonious representation strategy. Systematic reasoning errors and illusions can be identified with logical connectors (AND: 86 % valid initial models; XOR: 47 %; Wilcoxon z = 4.6; p < .001). Error rates were smallest when using two universal quantifiers (All-All), they increase significantly when using one (Some-All; All-Some) and again using none (Some-Some) (Page's L = 436; z = 3.40 p < .001). Although the different assertions allowed for multiple situations, the difficulty can be traced back to specific quantifiers and logical connectors.