Document Open Access Logo

Free Constructions and Coproducts of d-Frames

Authors Tomás Jakl, Achim Jung

PDF
Thumbnail PDF

File

LIPIcs.CALCO.2017.14.pdf
  • Filesize: 0.7 MB
  • 15 pages

Document Identifiers

Author Details

Tomás Jakl
Achim Jung

Cite AsGet BibTex

Tomás Jakl and Achim Jung. Free Constructions and Coproducts of d-Frames. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CALCO.2017.14

Abstract

A general theory of presentations for d-frames does not yet exist. We review the difficulties and give sufficient conditions for when they can be overcome. As an application we prove that the category of d-frames is closed under coproducts.
Keywords
  • Free construction
  • d-frame
  • coproduct
  • C-ideals

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. S. Abramsky. Domain theory in logical form. In Symposium on Logic In Computer Science, pages 47-53. IEEE Computer Society Press, 1987. Google Scholar
  2. Richard N. Ball and Aleš Pultr. Extending semilattices to frames using sites and coverages. Mathematica Slovaca, 64(3):527-544, 2014. Google Scholar
  3. B Banaschewski, GCL Brümmer, and KA Hardie. Biframes and bispaces. Quaestiones Mathematicae, 6(1-3):13-25, 1983. Google Scholar
  4. Bart Jacobs. Many-sorted coalgebraic modal logic: a model-theoretic study. RAIRO-Theoretical Informatics and Applications, 35(1):31-59, 2001. Google Scholar
  5. T. Jakl and A. Jung. Vietoris construction for bispaces and d-frames. In preparation. Google Scholar
  6. P. T. Johnstone. Stone Spaces, volume 3 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1982. Google Scholar
  7. A. Jung. Continuous domain theory in logical form. In B. Coecke, L. Ong, and P. Panangaden, editors, Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky, volume 7860 of Lecture Notes in Computer Science, pages 166-177. Springer Verlag, 2013. URL: http://dx.doi.org/10.1007/978-3-642-38164-5_12.
  8. A. Jung and M. A. Moshier. On the bitopological nature of Stone duality. Technical Report CSR-06-13, School of Computer Science, The University of Birmingham, 2006. 110 pages. URL: ftp://ftp.cs.bham.ac.uk/pub/tech-reports/2006/CSR-06-13.pdf.
  9. Bartek Klin. Coalgebraic modal logic beyond sets. Electronic Notes in Theoretical Computer Science, 173:177-201, 2007. Google Scholar
  10. Clemens Kupke, Alexander Kurz, and Yde Venema. Stone coalgebras. Theoretical Computer Science, 327(1-2):109-134, 2004. Google Scholar
  11. Jimmie Lawson. Stably compact spaces. Mathematical Structures in Computer Science, 21(01):125-169, 2011. Google Scholar
  12. Jorge Picado and Aleš Pultr. Frames and Locales: Topology without points. Springer-Birkhauser Basel, 2011. Google Scholar
  13. S. J. Vickers. Topology Via Logic, volume 5 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1989. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact