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PART A: Theoretical Issues 1. Visual Information and Valid Reasoning, Jon Barwise and John Etchemendy 2. Operational Constraints in Diagrammatic Reasoning, Atsushi Shimojima 3. Diagrams and the Concept of Logical System, Jon Barwise and Eric Hammer PART B: Case Studies 4. Situation-Theoretic Account of Valid Reasoning with Venn Diagrams, Sun-Joo Shin 5. Towards a Model Theory of Venn Diagrams, eric Hammer and Norman Danner 6. Peircean Graphs for Propositional Logic, Eric Hammer 7. A Diagrammatic Subsystem of Hilbert's Geometry, Isabel Luengo PART C: Heterogenous Systems 8. Heterogenous Logic, Jon Barwise and John Etchemendy 9. Toward the Rigorous Use of Diagrams in Reasoning about Hardware, Steven D. Johnson, Jon Barwise, and Gerard Allwein 10. Exploiting the Potential of Diagrams in Guiding Hardware Reasoning, Kathi D. Fisler