A Spatial Search Framework for Executing Perceptions and Actions in Diagrammatic Reasoning

Diagrammatic reasoning (DR) requires perceiving information from a diagram and modifying/creating objects in a diagram according to problem solving needs. The perceptions and actions in most DR systems are hand-coded for the specific application. The absence of a general framework for executing perceptions/actions poses as a major hindrance to using them opportunistically. Our goal is to develop a framework for executing a wide variety of specified perceptions and actions across tasks/domains without human intervention. We observe that the domain/task-specific perceptions/actions can be transformed into domain/task-independent spatial problems. In our framework, a human problem solver specifies a spatial problem as a quantified constraint satisfaction problem (QCSP) in the real domain using an open-ended vocabulary of properties, relations and actions involving three types of spatial objects – points, curves, regions. Traditional approaches solve such QCSPs by computing the equivalent quantifier-free algebraic expression, the complexity of which is inherently doubly exponential. In this paper, we investigate a domain-independent framework of spatial search for solving 2D spatial problems specified as QCSPs. The framework searches for the solution in the space of the diagram instead of in the space of algebraic equations/inequalities. We prove the correctness of our approach and show that it is more efficient than cylindrical algebraic decomposition, a well-known algebraic approach, by executing perceptions/actions in two army applications.