Phase semantic cut-elimination and normalization proofs of first- and higher-order linear logic
Theoretical Computer Science - Special issue on linear logic, 1
Logic and Visual Information
SD2: A Sound and Complete Diagrammatic Reasoning System
VL '00 Proceedings of the 2000 IEEE International Symposium on Visual Languages (VL'00)
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
Inductively Generating Euler Diagrams
IEEE Transactions on Visualization and Computer Graphics
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
A logical investigation on global reading of diagrams
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
The efficacy of diagrams in syllogistic reasoning: a case of linear diagrams
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
Syllogisms in Rudimentary Linear Logic, Diagrammatically
Journal of Logic, Language and Information
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Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in the standard approach, but in terms of topological relations between diagrammatic objects. We formalize the unification rule, which plays a central role in Euler diagrammatic reasoning, in a style of natural deduction. We prove the soundness and completeness theorems with respect to a formal set-theoretical semantics. We also investigate structure of diagrammatic proofs and prove a normal form theorem.