A Logical Framework for Spatial Mental Models

Abstract

In the psychology of reasoning, spatial reasoning capacities are often explained by postulating models in the mind. According to the Space To Reason theory, these models only consist of the spatial qualities of the considered situation, such as the topology or the relative orientation, without containing any quantitative measures. It turns out that a field of computer science, called Qualitative Spatial Reasoning, is entirely dedicated to formalizing such qualitative representations. Although the formalism of qualitative spatial reasoning has already been used in the space to reason theory, it has not yet entirely been exploited. Indeed, it can also be used to formally characterize spatial models and account for our reasoning on them. To exemplify this claim, two typical problems of spatial reasoning are exhaustively analyzed through the framework of qualitative constraint networks (QCN). It is shown that for both problems every aspect can be formally captured, as for example the integration of premises into one single model, or the prediction of alternative models. Therefore, this framework represents an opportunity to completely formalize the space to reason theory and, what is more, diversify the type of spatial reasoning accounted by it. The most substantial element of this formal translation is that a spatial model and a satisfiable atomic QCN - a scenario - turn out to have exactly the same conditions of possibility.