This course is about computational models of reasoning involving diagrams. A diagram is a form of visual representation, a kind of picture, but unlike sketches, color drawings and paintings, that emphasize qualitative aspects of the represented objects, diagrams focus more on structural and schematic aspects of objects and spatial states of affairs, and are used mostly for analysis and problem solving. Diagrams are very ubiquitous forms of representation and they are present in mathematics, logic, physics, engineering, architecture, urban planning, and many other scientific disciplines and human practices. This topic can be studied from a philosophical, psychological, design and computational perspectives, among others. In the present course, the subject is addressed from a computational perspective, and the focus is on computational models of diagrammatic reasoning implemented as Artificial Intelligence (AI) programs: programs that use diagrams in reasoning and problem solving task. To clarify the sense in which a computer program can represent a diagram (i.e. the external representation on a piece of paper) and reason and solve problems using such representation is one of the main motivations of this course.
Introduction to Diagrammatic Reasoning
The Imagery Debate
Propositional versus Analogical Representations in AI
Diagrammatic Identity, Intentionality and Visualization
Diagrammatic Representation and Interpretation
Heterogeneous Reasoning
Abstraction and the Expressivity of Diagrams
Geometric Description and the Concept of Space
Perceptual Inference and the Triangle of Imagery
Diagrammatic Action Schemes
Conservation Principles and Diagrammatic Derivations
Diagrammatic Induction
Applications of Diagrammatic Reasoning
Diagrams and Knowledge Representation