Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Relational and Multirelational Representation Theorems for Complete Idempotent Left Semirings

  • Conference paper
Relational and Algebraic Methods in Computer Science (RAMICS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6663))

  • 731 Accesses

Abstract

Brown and Gurr have shown a relational representation theorem for quantales. Complete idempotent left semirings are a relaxation of quantales by giving up strictness and distributivity of composition over arbitrary joins from the left. We show a relational representation theorem for them. Multirelations are generalisation of relations. We also show a multirelational representation theorem for complete idempotent left semirings.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Brown, C., Gurr, D.: A Representation Theorem for Quantales. Journal of Pure and Applied Algebra 85, 27–42 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chellas, B.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)

    Book  MATH  Google Scholar 

  3. Conway, J.: Regular Algebra and Finite Machines. Chapman and Hall, Boca Raton (1971)

    MATH  Google Scholar 

  4. McCune, W.: Prover9 and Mace4, http://www.cs.unm.edu/~mccune/mace4/ .

  5. Möller, B.: Lazy Kleene Algebra. In: Kozen, D. (ed.) MPC 2004. LNCS, vol. 3125, pp. 252–273. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Mulvey, C.J.: ”&”, Supplemento ai Rendiconti del Circolo Matematico di Palermo. Serie II (12), 99–104 (1986)

    Google Scholar 

  7. Nishizawa, K., Tsumagari, N., Furusawa, H.: The Cube of Kleene Algebras and the Triangular Prism of Multirelations. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds.) RelMiCS 2009. LNCS, vol. 5827, pp. 276–290. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Parikh, R.: Propositional logics of programs: new directions. In: Karpinski, M. (ed.) FCT 1983. LNCS, vol. 158, pp. 347–359. Springer, Heidelberg (1983)

    Chapter  Google Scholar 

  9. Rewitzky, I.: Binary multirelations. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.) Theory and Applications of Relational Structures as Knowledge Instruments. LNCS, vol. 2929, pp. 256–271. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Kagoshima University, Japan

    Hitoshi Furusawa

  2. Department of Information Systems, Tottori University of Environmental Studies, Japan

    Koki Nishizawa

Authors
  1. Hitoshi Furusawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Koki Nishizawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000, Tilburg, LE, The Netherlands

    Harrie de Swart

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Furusawa, H., Nishizawa, K. (2011). Relational and Multirelational Representation Theorems for Complete Idempotent Left Semirings. In: de Swart, H. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2011. Lecture Notes in Computer Science, vol 6663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21070-9_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21070-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21069-3

  • Online ISBN: 978-3-642-21070-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation