Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7860))

Abstract

In 1987 Samson Abramsky presented Domain Theory in Logical Form in the Logic in Computer Science conference. His contribution to the conference proceedings was honoured with the Test-of-Time award 20 years later. In this note I trace a particular line of research that arose from this landmark paper, one that was triggered by my collaboration with Samson on the article Domain Theory which was published as a chapter in the Handbook of Logic in Computer Science in 1994.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramsky, S.: The lazy lambda calculus. In: Turner, D. (ed.) Research Topics in Functional Programming, pp. 65–117. Addison Wesley (1990)

    Google Scholar 

  2. Abramsky, S.: A domain equation for bisimulation. Information and Computation 92, 161–218 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abramsky, S.: Domain theory in logical form. Annals of Pure and Applied Logic 51, 1–77 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  4. Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Semantic Structures. Handbook of Logic in Computer Science, vol. 3, pp. 1–168. Clarendon Press (1994)

    Google Scholar 

  5. Desharnais, J., Edalat, A., Panangaden, P.: A logical characterization of bisimulation for labeled Markov processes. In: 13th IEEE Symposium on Logic in Computer Science, Indianapolis 1998, pp. 478–489 (1998)

    Google Scholar 

  6. Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation for labelled Markov processes. Information and Computation 179, 163–193 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Escardó, M.H.: Synthetic topology of data types and classical spaces. In: Desharnais, J., Panangaden, P. (eds.) Domain-theoretic Methods in Probabilistic Processes. Electronic Notes in Theoretical Computer Science, vol. 87, pp. 21–156. Elsevier Science Publishers B.V. (2004)

    Google Scholar 

  8. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: A Compendium of Continuous Lattices. Springer (1980)

    Google Scholar 

  9. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: Continuous Lattices and Domains. Encyclopedia of Mathematics and its Applications, vol. 93. Cambridge University Press (2003)

    Google Scholar 

  10. Hennessy, M.C.B., Plotkin, G.D.: Full abstraction for a simple parallel programming language. In: Bečvář, J. (ed.) MFCS 1979. LNCS, vol. 74, pp. 108–120. Springer, Heidelberg (1979)

    Chapter  Google Scholar 

  11. Jung, A., Kegelmann, M., Moshier, M.A.: Stably compact spaces and closed relations. In: Brookes, S., Mislove, M. (eds.) 17th Conference on Mathematical Foundations of Programming Semantics. Electronic Notes in Theoretical Computer Science, vol. 45, 24 pages. Elsevier Science Publishers B.V. (2001)

    Google Scholar 

  12. Jung, A., Moshier, M.A.: On the bitopological nature of Stone duality. Technical Report CSR-06-13, School of Computer Science, The University of Birmingham, 110 pages (2006)

    Google Scholar 

  13. Jones, C., Plotkin, G.: A probabilistic powerdomain of evaluations. In: Proceedings of the 4th Annual Symposium on Logic in Computer Science, pp. 186–195. IEEE Computer Society Press (1989)

    Google Scholar 

  14. Jung, A., Sünderhauf, P.: On the duality of compact vs. open. In: Andima, S., Flagg, R.C., Itzkowitz, G., Misra, P., Kong, Y., Kopperman, R. (eds.) Papers on General Topology and Applications: Eleventh Summer Conference at the University of Southern Maine. Annals of the New York Academy of Sciences, vol. 806, pp. 214–230 (1996)

    Google Scholar 

  15. Jung, A., Tix, R.: The troublesome probabilistic powerdomain. In: Edalat, A., Jung, A., Keimel, K., Kwiatkowska, M. (eds.) Proceedings of the Third Workshop on Computation and Approximation. Electronic Notes in Theoretical Computer Science, vol. 13, 23 pages. Elsevier Science Publishers B.V. (1998)

    Google Scholar 

  16. Jung, A.: The classification of continuous domains. In: Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science, pp. 35–40. IEEE Computer Society Press (1990)

    Google Scholar 

  17. Jung, A.: Stably compact spaces and the probabilistic powerspace construction. In: Desharnais, J., Panangaden, P. (eds.) Domain-Theoretic Methods in Probabilistic Processes. Electronic Notes in Theoretical Computer Science, vol. 87, pp. 5–20. Elsevier Science Publishers B.V. (2004)

    Google Scholar 

  18. Kegelmann, M.: Continuous domains in logical form. PhD thesis, School of Computer Science, The University of Birmingham (1999)

    Google Scholar 

  19. Klinke, O.: A bitopological point-free approach to compactifications. PhD thesis, School of Computer Science, The University of Birmingham (2012)

    Google Scholar 

  20. Lawson, J.D.: The duality of continuous posets. Houston Journal of Mathematics 5, 357–394 (1979)

    MathSciNet  MATH  Google Scholar 

  21. Moshier, M.A., Jung, A.: A logic for probabilities in semantics. In: Bradfield, J.C. (ed.) CSL 2002. LNCS, vol. 2471, pp. 216–231. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  22. Plotkin, G.D.: Post-graduate lecture notes in advanced domain theory (incorporating the “Pisa Notes”). Dept. of Computer Science, Univ. of Edinburgh (1981)

    Google Scholar 

  23. Priestley, H.A.: Representation of distributive lattices by means of ordered Stone spaces. Bulletin of the London Mathematical Society 2, 186–190 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  24. Scott, D.S.: A type theoretic alternative to ISWIM, CUCH, OWHY. University of Oxford (1969) (manuscript)

    Google Scholar 

  25. Scott, D.S.: Continuous lattices. In: Lawvere, E. (ed.) Toposes, Algebraic Geometry and Logic. Lecture Notes in Mathematics, vol. 274, pp. 97–136. Springer (1972)

    Google Scholar 

  26. Scott, D.S.: A type-theoretical alternative to ISWIM, CUCH, OWHY. Theoretical Computer Science 121, 411–440 (1993); Reprint of a manuscript written in 1969

    Article  MathSciNet  MATH  Google Scholar 

  27. Saheb-Djahromi, N.: CPO’s of measures for nondeterminism. Theoretical Computer Science 12, 19–37 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  28. Smyth, M.B.: Effectively given domains. Theoretical Computer Science 5, 257–274 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  29. Smyth, M.B.: The largest cartesian closed category of domains. Theoretical Computer Science 27, 109–119 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  30. Smyth, M.B.: Power domains and predicate transformers: a topological view. In: Díaz, J. (ed.) ICALP 1983. LNCS, vol. 154, pp. 662–675. Springer, Heidelberg (1983)

    Chapter  Google Scholar 

  31. Smyth, M.B.: Stable compactification I. Journal of the London Mathematical Society 45, 321–340 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  32. Stone, M.H.: The theory of representations for Boolean algebras. Trans. American Math. Soc. 40, 37–111 (1936)

    MathSciNet  MATH  Google Scholar 

  33. Stone, M.H.: Topological representation of distributive lattices. Časopsis pro Pěstování Matematiky a Fysiky 67, 1–25 (1937)

    MATH  Google Scholar 

  34. Vickers, S.J.: Topology Via Logic. Cambridge Tracts in Theoretical Computer Science, vol. 5. Cambridge University Press (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Jung, A. (2013). Continuous Domain Theory in Logical Form. In: Coecke, B., Ong, L., Panangaden, P. (eds) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science, vol 7860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38164-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38164-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38163-8

  • Online ISBN: 978-3-642-38164-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics