Conceptual structures: information processing in mind and machine
Conceptual structures: information processing in mind and machine
Visual information and valid reasoning
Visualization in teaching and learning mathematics
Realization of a geometry-theorem proving machine
Computers & thought
The sciences of the artificial (3rd ed.)
The sciences of the artificial (3rd ed.)
Logic and Visual Information
Diagrammatic Reasoning: Cognitive and Computational Perspectives
Diagrammatic Reasoning: Cognitive and Computational Perspectives
On the Use of the Constructive Omega-Rule within Automated Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Editorial: Efficacy of Diagrammatic Reasoning
Journal of Logic, Language and Information
A Proposal for Automating Diagrammatic Reasoning in Continuous Domains
Diagrams '00 Proceedings of the First International Conference on Theory and Application of Diagrams
Diagrammatic Reasoning in Separation Logic
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
The well-designed young mathematician
Artificial Intelligence
Heterogeneous reaoning in real arithmetics
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Heterogeneous proofs: spider diagrams meet higher-order provers
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Speedith: a diagrammatic reasoner for spider diagrams
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
European collaboration on automated reasoning
AI Communications - ECAI 2012 Turing and Anniversary Track
Biological, computational and robotic connections with Kant's theory of mathematical knowledge
AI Communications - ECAI 2012 Turing and Anniversary Track
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Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an intuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather than general diagrams are used to prove particular concrete instances of the universally quantified theorem. The diagrammatic proof is captured by the use of geometric operations on the diagram. These operations are the ’’inference steps‘‘ of the proof. An abstracted schematic proof of the universally quantified theorem is induced from these proof instances. The constructive ω-rule provides the mathematical basis for this step from schematic proofs to theoremhood. In this way we avoid the difficulty of treating a general case in a diagram. One method of confirming that the abstraction of the schematic proof from the proof instances is sound is proving the correctness of schematic proofs in the meta-theory of diagrams. These ideas have been implemented in the system, called Diamond, which is presented here.