A theory and a computational model of spatial reasoning with preferred mental models

Abstract

Inferences about spatial arrangements and relations like "The Porsche is parked to the left of the Dodge and the Ferrari is parked to the right of the Dodge, thus, the Porsche is parked to the left of the Ferrari," are ubiquitous. However, spatial descriptions are often interpretable in many different ways and compatible with several alternative mental models. This article suggests that individuals tackle such indeterminate multiple-model problems by constructing a single, simple, and typical mental model but neglect other possible models. The model that first comes to reasoners' minds is the preferred mental model. It helps save cognitive resources but also leads to reasoning errors and illusory inferences. The article presents a preferred model theory and an instantiation of this theory in the form of a computational model, preferred inferences in reasoning with spatial mental models (PRISM). PRISM can be used to simulate and explain how preferred models are constructed, inspected, and varied in a spatial array that functions as if it were a spatial working memory. A spatial focus inserts tokens into the array, inspects the array to find new spatial relations, and relocates tokens in the array to generate alternative models of the problem description, if necessary. The article also introduces a general measure of difficulty based on the number of necessary focus operations (rather than the number of models). A comparison with results from psychological experiments shows that the theory can explain preferences, errors, and the difficulty of spatial reasoning problems.