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.

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1. Introduction to Diagrammatic Reasoning

2. The Imagery Debate

3. Propositional versus Analogical Representations in AI

4. Diagrammatic Identity, Intentionality and Visualization

5. Diagrammatic Representation and Interpretation

6. Heterogeneous Reasoning

7. Abstraction and the Expressivity of Diagrams

8. Geometric Description and the Concept of Space

9. Perceptual Inference and the Triangle of Imagery

10. Diagrammatic Action Schemes

11. Conservation Principles and Diagrammatic Derivations

12. Diagrammatic Induction

13. Applications of Diagrammatic Reasoning

14. Diagrams and Knowledge Representation