Spatial problem solving for diagrammatic reasoning

Diagrammatic reasoning (DR) is pervasive in human problem solving as a powerful adjunct to symbolic reasoning based on language-like representations. However, Artificial Intelligence is overwhelmingly based on symbolic representations, with proportionately scant attention to diagrams. This dissertation is a contribution to building artificial agents that can create and use diagrams as part of their problem solving. The work is in a framework in which DR is modeled as a process in which subtasks are solved, as appropriate, either by inference from symbolic representations or by information perceived from a diagram, and subtasks may also act on the diagram, i.e., create or modify objects in the diagram. The perceptions and actions are in fact domain- and task-specific 2D spatial problems defined in terms of properties and relations involving diagrammatic objects. Most DR systems built so far are task-specific, and their developers as a rule have hand-crafted the required perceptions and actions. Our goal is the development of a general, i.e., domain- and task-independent, capability that takes specifications of perceptions and actions and automatically executes them. Thus, the purpose of this dissertation is to investigate: (1) A language for a human problem solver to communicate a wide variety of 2D spatial problems relevant to DR, and (2) A general domain-independent framework of underlying representations and reasoning strategies suitable for efficiently solving spatial problems without human intervention. This dissertation will present a high-level language that is extensible, human-usable, and expressive enough to describe a wide variety of spatial problems in terms of constraints. The constraints are specified in first-order logic over the real domain using a vocabulary of objects, properties, relations and actions. Two general and independent strategies—constraint satisfaction and spatial search—are developed for automatically solving the spatial problems specified in that language. Several ideas about how to make these strategies computationally efficient are proposed and illustrated by examples. A traditional AI problem solver is augmented with this spatial problem solver for reasoning with diagrams in different domains for real-world applications. The utility of the framework is judged by the expressiveness of the language, and generality and efficiency of the two strategies.