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Sequent Calculus for Euler Diagrams

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)peer-review

Published
Publication date18/06/2018
Host publicationDiagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings
EditorsPeter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz, Francesco Bellucci
Place of PublicationCham
PublisherSpringer
Pages399-407
Number of pages9
ISBN (Electronic)9783319913766
ISBN (Print)9783319913759
<mark>Original language</mark>English

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume10871
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Abstract

Proof systems play a major role in the formal study of diagrammatic logical systems. Typically, the style of inference is not directly comparable to traditional sentential systems, to study the diagrammatic aspects of inference. In this work, we present a proof system for Euler diagrams with shading in the style of sequent calculus. We prove it to be sound and complete. Furthermore we outline how this system can be extended to incorporate heterogeneous logical descriptions. Finally, we explain how small changes allow for reasoning with intuitionistic logic.