Humans employ diagrams and other pictures, both real and imagined, as aids to reasoning, and many kinds of problems are solved by an interaction between propositional reasoning and spatial imagery. This research will explore computational explanations of this ability. The use of diagrams is in part a form of spatial reasoning, which is the use of representations of objects in space for problem-solving, inferring, and learning. Spatial reasoning is an important ability of humans, and machines with similar capacities will have certain advantages over machines without them, including a more natural mode of interaction with people. The proposed research hypothesizes that these are forms of representation that aid human reasoning by providing psychologically and computationally efficient ways of capturing and propagating the constraints of real world events and mathematical abstractions. The creation, modification and transformation of these representations allow a person to perform mental experiments that make deductions and test conjectures about the corresponding physical situations and mathematical relations. The ultimate result of this research could be a better scientific understanding of the psychology of reasoning with imagery, and the basis of a technology for machines that can think directly in images.//
