Skip to main content

Creating a Second Order Diagrammatic Logic

  • Conference paper
Diagrammatic Representation and Inference (Diagrams 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6170))

Included in the following conference series:

Abstract

Many of the formal diagrammatic logics that have been developed are limited to be first order (typically monadic). This means that such logics cannot define commonly occurring concepts and, thus, are not as widely applicable as we might like. Suitably increasing their expressiveness will allow both the formalization of second order concepts and the study of such concepts from a new perspective. Our aim is to produce a second order diagrammatic logic and we present the initial ideas towards the development of such a logic.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dau, F., Ekland, P.: A diagrammatic reasoning system for the description logic \(\mathcal{ACL}\). Journal of Visual Languages and Computing 19(5), 539–573 (2008)

    Article  Google Scholar 

  2. Delaney, A., Taylor, J., Thompson, S.: Spider diagrams of order and a hierarchy of star-free regular languages. In: Stapleton, G., Howse, J., Lee, J. (eds.) Diagrams 2008. LNCS (LNAI), vol. 5223, pp. 172–187. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS Journal of Computation and Mathematics 8, 145–194 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kent, S.: Constraint diagrams: Visualizing invariants in object oriented modelling. In: Proceedings of OOPSLA 1997, pp. 327–341. ACM Press, New York (1997)

    Google Scholar 

  5. Shin, S.-J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  6. Stapleton, G., Masthoff, J.: Incorporating negation into visual logics: A case study using Euler diagrams. In: Visual Languages and Computing 2007, pp. 187–194. Knowledge Systems Institute (2007)

    Google Scholar 

  7. Swoboda, N., Allwein, G.: Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference. Journal on Software and System Modeling 3(2), 136–149 (2004)

    Article  Google Scholar 

  8. Thomas, W.: Classifying regular events in symbolic logic. Journal of Computer and System Sciences 25, 360–376 (1982)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chapman, P., Stapleton, G. (2010). Creating a Second Order Diagrammatic Logic. In: Goel, A.K., Jamnik, M., Narayanan, N.H. (eds) Diagrammatic Representation and Inference. Diagrams 2010. Lecture Notes in Computer Science(), vol 6170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14600-8_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14600-8_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14599-5

  • Online ISBN: 978-3-642-14600-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics