Abstract
Diagonal arguments lie at the root of many fundamental phenomena in the foundations of logic and mathematics. Recently, a striking form of diagonal argument has appeared in the foundations of epistemic game theory, in a paper by Adam Brandenburger and H. Jerome Keisler [11]. The core Brandenburger-Keisler result can be seen, as they observe, as a two-person or interactive version of Russell’s Paradox.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Abramsky, S.: Retracing Some Paths in Process Algebra. In: CONCUR 1996. LNCS, vol. 1119, pp. 1–17. Springer, Heidelberg (1996)
Abramsky, S.: A Cook’s tour of the finitary non-well-founded sets. In: Artemov, S., Barringer, H., d’Avila Garcez, A., Lamb, L.C., Woods, J. (eds.) We Will Show Them: Essays in Honour of Dov Gabbay, vol. 1, pp. 1–18. College Publications (2005)
Abramsky, S.: Coalgebras, Chu spaces, and representations of physical systems. In: 2010 25th Annual IEEE Symposium on Logic in Computer Science, LICS, pp. 411–420. IEEE (2010)
Abramsky, S., Jagadeesan, R.: New foundations for the geometry of interaction. Information and Computation 111(1), 53–119 (1994)
Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, pp. 1–168. Oxford University Press (1994)
Abramsky, S., Melliés, P.-A.: Concurrent games and full completeness. In: Proceedings of the Fourteenth International Symposium on Logic in Computer Science, pp. 431–442. IEEE Computer Society Press (1999)
Aczel, P., Mendler, N.P.: A Final Coalgebra Theorem. In: Dybjer, P., Pitts, A.M., Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds.) Category Theory and Computer Science. LNCS, vol. 389, pp. 357–365. Springer, Heidelberg (1989)
Barr, M.: Terminal coalgebras in well-founded set theory. Theor. Comput. Sci. 114(2), 299–315 (1993)
Battigalli, P., Siniscalchi, M.: Strong belief and forward-induction reasoning. Journal of Economic Theory 106, 356–391 (2002)
Brandenburger, A., Friedenberg, A., Keisler, H.J.: Admissibility in games. Econometrica 76, 307–352 (2008)
Brandenburger, A., Jerome Keisler, H.: An impossibility theorem on beliefs in games. Studia Logica 84(2), 211–240 (2006)
Butz, C.: Regular categories and regular logic. Technical Report LS-98-2, BRICS (October 1998)
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)
Harsanyi, J.C.: Games with incomplete information played by ”Bayesian” players, I–III. Part I. The basic model. Management Science 14(3) (1967)
Heifetz, A., Samet, D.: Topology-free typology of beliefs. Journal of Economic Theory 82, 324–381 (1998)
Kupke, C., Kurz, A., de Venema, Y.: Stone coalgebras. Theor. Comput. Sci. 327(1-2), 109–134 (2004)
William Lawvere, F.: Diagonal arguments and cartesian closed categories. Lecture Notes in Mathematics, vol. 92, pp. 134–145 (1969)
Michael, E.: Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71, 152–182 (1951)
Moss, L.S., Viglizzo, I.D.: Final coalgebras for functors on measurable spaces. Inf. Comput. 204(4), 610–636 (2006)
Pacuit, E.: Understanding the Brandenburger-Keisler paradox. Studia Logica 86(3), 435–454 (2007)
Rutten, J.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000)
Soto-Andrade, J., Varela, F.J.: Self-reference and fixed points: a discussion and an extension of Lawvere’s theorem. Acta Applicandae Mathematicae 2, 1–19 (1984)
van Oosten, J.: Basic category theory. Technical Report LS-95-1, BRICS (January 1995)
Worrell, J.: Terminal sequences for accessible endofunctors. Electr. Notes Theor. Comput. Sci. 19 (1999)
Yanofsky, N.S.: A universal approach to self-referential paradoxes and fixed points. Bulletin of Symbolic Logic 9(3), 362–386 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 IFIP International Federation for Information Processing
About this paper
Cite this paper
Abramsky, S., Zvesper, J. (2012). From Lawvere to Brandenburger-Keisler: Interactive Forms of Diagonalization and Self-reference. In: Pattinson, D., Schröder, L. (eds) Coalgebraic Methods in Computer Science. CMCS 2012. Lecture Notes in Computer Science, vol 7399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32784-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-32784-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32783-4
Online ISBN: 978-3-642-32784-1
eBook Packages: Computer ScienceComputer Science (R0)