Information flow: the logic of distributed systems
Information flow: the logic of distributed systems
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Theories of Diagrammatic Reasoning: Distinguishing Component Problems
Minds and Machines
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
A Diagrammatic Inference System with Euler Circles
Journal of Logic, Language and Information
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In the literature on diagrammatic reasoning, Venn diagrams are abstractly formalized in terms of minimal regions. In view of the cognitive process to recognize Venn diagrams, we modify slightly the formalization by distinguishing conjunctive, negative, and disjunctive regions among possible regions in Venn diagrams. Then we study a logic translation of the Venn diagrammatic system with the aim of investigating how our inference rules are rendered to resolution calculus. We further investigate the free ride property of the Venn diagrammatic system. Free ride is one of the most basic properties of diagrammatic systems and it is mainly discussed in cognitive science literature as an account of the inferential efficacy of diagrams. The soundness of our translation shows that a free ride occurs between the Venn diagrammatic system and resolution calculus. Furthermore, our translation provides a more in-depth analysis of the free ride. In particular, we calculate how many pieces of information are obtained in the manipulation of Venn diagrams.