Document Open Access Logo

Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games

Author Christof Spanring

PDF
Thumbnail PDF

File

OASIcs.ICCSW.2014.91.pdf
  • Filesize: 0.58 MB
  • 8 pages

Document Identifiers

Author Details

Christof Spanring

Cite As Get BibTex

Christof Spanring. Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games. In 2014 Imperial College Computing Student Workshop. Open Access Series in Informatics (OASIcs), Volume 43, pp. 91-98, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014) https://doi.org/10.4230/OASIcs.ICCSW.2014.91

Abstract

In this work we investigate infinite structures. We discuss the importance, meaning and temptation of the axiom of choice and equivalent formulations with respect to graph theory, abstract argumentation and dialogue games. Emphasis is put on maximal independent sets in graph
theory as well as preferred semantics in abstract argumentation.

Subject Classification

Keywords
  • axiom of choice
  • graph theory
  • maximal independent sets
  • abstract argumentation
  • dialogue games

Metrics

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

References

  1. Pietro Baroni and Massimiliano Giacomin. Semantics of abstract argument systems. In Iyad Rahwan and Guillermo Ricardo Simari, editors, Argumentation in Artificial Intelligence, chapter 2, pages 25-44. Springer, 2009. Google Scholar
  2. Trevor J. M. Bench-Capon, Sylvie Doutre, and Paul E. Dunne. Asking the right question: forcing commitment in examination dialogues. In Philippe Besnard, Sylvie Doutre, and Anthony Hunter, editors, Proceedings of the 2nd Conference on Computational Models of Argument (COMMA 2008), volume 172, pages 49-60. IOS Press, 2008. Google Scholar
  3. Béla Bollobás. Modern graph theory, volume 184. Springer, 1998. Google Scholar
  4. Martin Caminada and Dov M. Gabbay. A logical account of formal argumentation. Studia Logica, 93(2):109-145, 2009. Google Scholar
  5. Martin Caminada and Bart Verheij. On the existence of semi-stable extensions. In Proceedings of the 22nd Benelux Conference on Artificial Intelligence, 2010. Google Scholar
  6. Paul J Cohen. The independence of the continuum hypothesis. Proceedings of the National Academy of Sciences of the United States of America, 50(6):1143, 1963. Google Scholar
  7. Keith Devlin. The Joy of Sets: Fundamentals of Contemporary Set Theory. Undergraduate Texts in Mathematics. Springer, Springer-Verlag 175 Fifth Avenue, New York, New York 10010, U.S.A., 2nd edition, 1994. Google Scholar
  8. Phan Minh Dung. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell., 77(2):321-358, 1995. Google Scholar
  9. Harvey M. Friedman. Invariant maximal cliques and incompleteness, 2011. Google Scholar
  10. Kurt Gödel. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatsh. Math. Phys., 38(1):173-198, 1931. Google Scholar
  11. Kurt Gödel and George William Brown. The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory. Princeton University Press, 1940. Google Scholar
  12. Charles Leonard Hamblin. Fallacies. Methuen London, 1970. Google Scholar
  13. Thomas Jech. About the axiom of choice. Handbook of mathematical logic, 90:345-370, 1977. Google Scholar
  14. Thomas Jech. Set Theory. Springer, 3rd edition, 2006. Google Scholar
  15. Kenneth Kunen. Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics). North Holland, 1983. Google Scholar
  16. Peter McBurney and Simon Parsons. Dialogue games for agent argumentation. In Argumentation in artificial intelligence, pages 261-280. Springer, 2009. Google Scholar
  17. Jan Mycielski. On the axiom of determinacy. Fund. Math, 53:205-224II, 1964. Google Scholar
  18. Rudy Rucker. Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library). Princeton University Press, 2004. Google Scholar
  19. Lajos Soukup. Infinite combinatorics: from finite to infinite. In Horizons of combinatorics, pages 189-213. Springer, 2008. Google Scholar
  20. Stephen Toulmin. The Uses of Argument. Cambridge University Press, 2003. Google Scholar
  21. Gerard AW Vreeswik and Henry Prakken. Credulous and sceptical argument games for preferred semantics. In Logics in Artificial Intelligence, pages 239-253. Springer, 2000. Google Scholar
  22. Douglas N Walton. Logical Dialogue-Games. University Press of America, Lanham, Maryland, 1984. Google Scholar
  23. Douglas Brent West et al. Introduction to graph theory, volume 2. Prentice hall Upper Saddle River, 2001. 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 About DROPS Imprint Privacy Contact