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Diagrams and Nonmonotonic Logic: What Is the Cognitive Relation? Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Sequent Calculus for Euler Diagrams

Author : Sven Linker

Published in: Diagrammatic Representation and Inference

Publisher: Springer International Publishing

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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.

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Footnotes
1
Compare with the textbook by Negri et al. [9].
 
2
More precisely, these logics are typically defined by the lack of these rules.
 
Literature
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Alves, S., Fernández, M., Mackie, I.: A new graphical calculus of proofs. In: Echahed, R. (ed.) TERMGRAPH 2011, vol. 48, pp. 69–84 (2011)
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Barwise, J., Etchemendy, J.: Heterogeneous logic. In: Logical Reasoning with Diagrams, pp. 179–200. Oxford University Press Inc. (1996)
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Burton, J., Stapleton, G., Howse, J.: Completeness proof strategies for Euler diagram logics. In: Euler Diagrams 2012, vol. 854, pp. 2–16. CEUR (2012)
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Linker, S., Burton, J., Jamnik, M.: Tactical diagrammatic reasoning. In: UITP 2016. EPTCS, vol. 239, pp. 29–42. Open Publishing Association (2017)
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Negri, S., von Plato, J., Ranta, A.: Structural Proof Theory. Cambridge University Press, Cambridge (2001)CrossRef
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Shin, S.J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1995)CrossRef
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Stapleton, G., Masthoff, J.: Incorporating negation into visual logics: a case study using Euler diagrams. In: VLC 2007, pp. 187–194. Knowledge Systems Institute (2007)
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Urbas, M., Jamnik, M., Stapleton, G.: Speedith: a reasoner for spider diagrams. J. Log. Lang. Inform. 24(4), 487–540 (2015)MathSciNetCrossRef
Metadata
Title
Sequent Calculus for Euler Diagrams
Author
Sven Linker
Copyright Year
2018
Book
Diagrammatic Representation and Inference

Print ISBN: 978-3-319-91375-9

Electronic ISBN: 978-3-319-91376-6

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91376-6_37