A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Automated Theorem Proving in Euler Diagram Systems
Journal of Automated Reasoning
Diagrammatic Reasoning System with Euler Circles: Theory and Experiment Design
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
A Survey of Reasoning Systems Based on Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
The efficacy of euler and Venn diagrams in deductive reasoning: empirical findings
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Two types of diagrammatic inference systems: natural deduction style and resolution style
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Two types of diagrammatic inference systems: natural deduction style and resolution style
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
A Diagrammatic Inference System with Euler Circles
Journal of Logic, Language and Information
Proof-Theoretical investigation of venn diagrams: a logic translation and free rides
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
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Since the 1990s, reasoning with Venn and Euler diagrams has been studied from mathematical and logical viewpoints. The standard approach to a formalization is a "region-based" approach, where a diagram is defined as a set of regions. An alternative is a "relation-based" approach, where a diagram is defined in terms of topological relations (inclusion and exclusion) between circles and points. We compare these two approaches from a proof-theoretical point of view. In general, diagrams correspond to formulas in symbolic logic, and diagram manipulations correspond to applications of inference rules in a certain logical system. From this perspective, we demonstrate the following correspondences. On the one hand, a diagram construed as a set of regions corresponds to a disjunctive normal form formula and the inference system based on such diagrams corresponds to a resolution calculus. On the other hand, a diagram construed as a set of topological relations corresponds to an implicational formula and the inference system based on such diagrams corresponds to a natural deduction system. Based on these correspondences, we discuss advantages and disadvantages of each framework.