Titlebook: Visual Reasoning with Diagrams; Amirouche Moktefi,Sun-Joo Shin Book 2013 Springer Basel 2013 diagrammatic reasoning.logic based on diagram

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On the Completeness of Spider Diagrams Augmented with Constants,ecific individuals. We give a formal syntax and semantics for the extended diagram language before introducing a collection of reasoning rules encapsulating logical equivalence and logical consequence. We prove that the resulting logic is sound, complete and decidable.

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What is a Logical Diagram?,ments in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously—as more than a mere ‘heuristic aid’ to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a cleanly definable se

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A Diagrammatic Calculus of Syllogisms,s by calculation. The calculus at issue allows the easy retrieving of the traditional rules of the syllogism and of the laws of the square of opposition. Moreover, it extends to .-term syllogisms and to syllogisms with complemented terms. In this respect, a comparison with De Morgan’s . is treated.

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On the Completeness of Spider Diagrams Augmented with Constants,ical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that represent specific individuals. We give a formal syntax and semantics for the extended diagram language before introducing a collection of reasoning rules encapsu

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