Skip to main content
SpringerLink
Log in

Domain and Antidomain Semigroups

  • Conference paper
Book cover Relations and Kleene Algebra in Computer Science (RelMiCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5827))

Included in the following conference series:

Abstract

We axiomatise and study operations for relational domain and antidomain on semigroups and monoids. We relate this approach with previous axiomatisations for semirings, partial transformation semigroups and dynamic predicate logic.

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

Access this chapter

Log in via an institution
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.

References

  1. Desharnais, J., Struth, G.: Modal semirings revisited. In: Audebaud, P., Paulin-Mohring, C. (eds.) MPC 2008. LNCS, vol. 5133, pp. 360–387. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Desharnais, J., Struth, G.: Domain Axioms for a Family of Near-Semirings. In: Meseguer, J., Roşu, G. (eds.) AMAST 2008. LNCS, vol. 5140, pp. 330–345. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Frink, O.: Pseudo-complements in semilattices. Duke Mathematics Journal 29, 500–515 (1962)

    Article  MathSciNet  Google Scholar 

  4. Hollenberg, M.: An equational axiomatization of dynamic negation and relational composition. Journal of Logic, Language and Information 6, 381–401 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Jackson, M., Stokes, T.: An invitation to C-semigroups. Semigroup Forum 62, 279–310 (2001)

    MATH  MathSciNet  Google Scholar 

  6. Jackson, M., Stokes, T.: Semilattice pseudo-complements on semigroups. Comm. Algebra 32, 2895–2918 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Jackson, M., Stokes, T.: Partial maps with domain and range: extending Schein’s representation. Comm. Algebra (to appear)

    Google Scholar 

  8. Jipsen, P., Struth, G.: The structure of the one-generated free domain semiring. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS/AKA 2008. LNCS, vol. 4988, pp. 234–242. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. McCune, W.: Prover9 / Mace4 (2007), www.prover9.org

  10. Möller, B., Struth, G.: Algebras of modal operators and partial correctness. Theoretical Computer Science 351, 221–239 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Schein, B.M.: Relation algebras and function semigroups. Semigroup Forum 1, 1–62 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  12. Schweizer, B., Sklar, A.: Function systems. Math. Annalen 172, 1–16 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  13. Trokhimenko, V.S.: Menger’s function systems, Izv. Vysš. Učebn. Zaved. Matematika 11(138), 71–78 (in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département d’informatique et de génie logiciel, Université Laval, Canada

    Jules Desharnais

  2. Department of Mathematics and Computer Science, Chapman University, USA

    Peter Jipsen

  3. Department of Computer Science, University of Sheffield, UK

    Georg Struth

Authors
  1. Jules Desharnais
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Jipsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Georg Struth
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Rudolf Berghammer

  2. College of Engineering, Qatar University, P.O. Box 2713, CSE 209, Doha, Qatar,  

    Ali Mohamed Jaoua

  3. Institut für Informatik, Universität Augsburg, Universitätsstr. 6a, 86135, Augsburg, Germany

    Bernhard Möller

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Desharnais, J., Jipsen, P., Struth, G. (2009). Domain and Antidomain Semigroups. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2009. Lecture Notes in Computer Science, vol 5827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04639-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04639-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04638-4

  • Online ISBN: 978-3-642-04639-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation