Skip to main content

Relational Formalisations of Compositions and Liftings of Multirelations

  • Conference paper
  • First Online:
  • 407 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9348))

Abstract

Multirelations are studied as a semantic domain for computing systems involving two dual kinds of nondeterminism. This paper presents relational formalisations of Kleisli, Parikh and Peleg’s compositions and liftings of multirelations.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Back, R.-J., von Wright, J.: Refinement Calculus: A Systematic Introduction. Springer (1998)

    Book  MATH  Google Scholar 

  2. Chandra, A.K., Kozen, D., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  3. Freyd, P., Scedrov, A.: Categories, allegories. North-Holland, Amsterdam (1990)

    MATH  Google Scholar 

  4. Furusawa, H., Kawahara, Y.: Point axioms and related conditions in Dedekind categories. J. Log. Algebr. Meth. Program 84(3), 359–376 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Furusawa, H., Struth, G.: Concurrent Dynamic Algebra. ACM Transactions on Computational Logic (in Press)

    Google Scholar 

  6. Furusawa, H., Struth, G.: Taming Multirelations. CoRR abs/1501.05147 (2015)

    Google Scholar 

  7. Goldblatt, R.: Parallel Action: Concurrent Dynamic Logic with Independent Modalities. Studia Logica 51(3/4), 551–578 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mac Lane, S.: Categories for the working mathematician. Springer (1971)

    Google Scholar 

  9. Martin, C.E., Curtis, S.A.: The algebra of multirelations. Mathematical Structures in Computer Science 23(3), 635–674 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Olivier, J.-P., Serrato, D.: Catégories de Dedekind. Morphismes dans les Catégories de Schröder. C. R. Acad. Sci. Paris 260, 939–941 (1980)

    MathSciNet  MATH  Google Scholar 

  11. Parikh, R.: Propositional Game Logic. In: FOCS 1983, pp. 195–200. IEEE Computer Society (1983)

    Google Scholar 

  12. Peleg, D.: Communication in Concurrent Dynamic Logic. J. Comput. Syst. Sci. 35(1), 23–58 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Peleg, D.: Concurrent dynamic logic. J. ACM 34(2), 450–479 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  14. Schmidt, G.: Relational Mathematics. Encyclopedia of Mathematics and its Applications, vol. 132. Cambridge University Press (2011)

    Google Scholar 

  15. Tsumagari, N.: Probability meets Non-Probability via Complete IL-Semi-rings. Ph.D. Thesis, Graduate School of Science and Engineering, Kagoshima University, Japan (2012)

    Google Scholar 

  16. van Benthem, J., Ghosh, S., Liu, F.: Modelling simultaneous games in dynamic logic. Synthese 165(2), 247–268 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hitoshi Furusawa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Furusawa, H., Kawahara, Y., Struth, G., Tsumagari, N. (2015). Relational Formalisations of Compositions and Liftings of Multirelations. In: Kahl, W., Winter, M., Oliveira, J. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2015. Lecture Notes in Computer Science(), vol 9348. Springer, Cham. https://doi.org/10.1007/978-3-319-24704-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24704-5_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24703-8

  • Online ISBN: 978-3-319-24704-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics