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Summary: In Defense of Euclidean Proof
Edward T. Dean1
August 8, 2008
1This thesis is a report on joint work carried out with Jeremy Avigad and John
Mumma.
ii
Contents
1 Introduction 1
2 The Diagrammatic Proof System E 5
2.1 Syntax and Structure of Proofs . . . . . . . . . . . . . . . . . 5
2.2 Logical Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Construction Rules . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Demonstration Rules . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Derived Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6 A Conservative Extension . . . . . . . . . . . . . . . . . . . . 16
3 Illustrative Constructions in E 17
3.1 Some Elements . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Some More Technical Constructions . . . . . . . . . . . . . . . 19
4 The Adequacy of E 23
4.1 What Form Completeness? . . . . . . . . . . . . . . . . . . . . 23
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