Contained in:
  • Eirene e Atena
  • Edited by Fulvio Attinà, Luciano Bozzo, Marco Cesa, Sonia Lucarelli
Book Chapter

Nabladot Analysis of Hybrid Theories in International Relations

  • Claudio Cioffi-Revilla

Scientific research in International Relations has produced a growing corpus of empirically grounded formal theoretical models of phenomena ranging from deterrence to systemic polarity, from conditions of peace to the onset of war. Many of these important theories contain a mix of continuous and discrete dimensions, causal variables, and parameters. Analysis and understanding of this fundamental and intriguing class of theories containing functions with a mix of continuous and discrete variables has puzzled generations of social scientists and applied mathematicians. This challenging and longstanding puzzle now has a solution. Here we demonstrate how the recently created calculus with nabladot operators is beginning to uncover previously unknown properties of hybrid international phenomena. Results include new concepts and precise principles on causal relationships, previously unknown political features, and fundamental properties of probabilistic causality, demonstrated through nabladot analysis of international events, crisis dynamics, and warfare.

  • Keywords:
  • international relations theory,
  • formal models,
  • nabladot calculus,
  • crises,
  • warfare,
+ Show More

Claudio Cioffi-Revilla

George Mason University, United States - ORCID: 0000-0001-6445-9433

  1. Ashford, Oliver M., H. Charnock, P. G. Drazin, J. C. R. Hunt, Paul Smoker, and Ian Sutherland, eds. 1993. The Collected Papers of Lewis Fry Richardson, Volume 2: Quantitative Psychology and Studies of Conflict. Cambridge, UK: Cambridge University Press.
  2. Bittinger, Marvin L., and J. Conrad Crown. 1981. Mathematics: a modeling approach. Reading, Massachusetts: Addison-Wesley.
  3. Boulding, Kenneth E. 1962. Conflict and Defense: A General Theory. New York: Harper and Row.
  4. Bruschi, Alessandro. 1990. Conoscenza e metodo: introduzione alla metodologia delle scienze sociali [Knowledge and method: introduction to the methodology of the social sciences]. Milano: Edizioni Scolastiche Bruno Mondadori.
  5. Cioffi-Revilla Claudio. 2014. “Theoretical Nabladot Analysis of Amdahl’s Law for Agent-Based Simulations.” In Euro-Par 2014: Parallel Processing Workshops, edited by Lopes L. et al. Lecture Notes in Computer Science, vol. 8805, 440–51. Cham, Switzerland:
  6. Cioffi-Revilla, Claudio. 1979. “Formal International Relations Theory: An Inventory, Review, and Integration.” PhD diss., State University of New York at Buffalo. Proquest 7913870.
  7. Cioffi-Revilla, Claudio. 1998. Politics and uncertainty: theory, models and applications. Cambridge, UK: Cambridge University Press.
  8. Cioffi-Revilla, Claudio. 2017. “On the exact calculus of hybrid functions.” Proceedings of the American Mathematical Society, Southeastern Regional Meeting, University of Central Florida, Orlando, Florida, September 23, 2017.
  9. Cioffi-Revilla, Claudio. 2019. “The nabladot operator for integrated calculus of hybrid functions with continuous and discrete variables.” Abstracts of Papers Presented to the American Mathematical Society 40/1, 195 (Winter): 201.
  10. Cioffi-Revilla, Claudio. 2020. “Hybrid Functions in the Sciences and Applied Mathematics.” SSRN <https://ssrn.com/abstract=3579413> (aaaa-mm-gg). DOI: 10.13140/RG.2.2.14376.11526
  11. Cioffi-Revilla, Claudio. 2021. Unified calculus of hybrid functions in the sciences and applied mathematics. Monograph ms (in press).
  12. Deutsch, Karl W. 19782. The Analysis of International Relations. Englewood Cliffs, New Jersey: Prentice-Hall. Internet Archive: analysisofintern0000deut.
  13. Eells, Ellery. 1991. Probabilistic causality. Vol. 1. Cambridge University Press.
  14. Gillespie, John V. 1976. “Why mathematical models?” In Mathematical Models in International Relations, edited by Dina A. Zinnes and John V. Gillespie, 37–61. New York: Praeger.
  15. Goertz, Gary, and Harvey Starr, eds. 2003. Necessary Conditions. Lanham, Maryland: Rowman & Littlefield.
  16. Gori, Umberto. 2004. Lezioni di Relazioni Internazionali. Padova: Cedam.
  17. Horvath, William J., and Caxton C. Foster. 1963. “Stochastic models of war alliances.” Journal of Conflict Resolution 7 (2): 110–16.
  18. Kline, Morris. 1985. Mathematics and the Search for Knowledge. Oxford-New York: Oxford University Press.
  19. Kolmogorov, Andrey. 1933. Grundbegriffe der Wahrscheinlichkeitsrechnung (in German). Berlin: Julius Springer. Translation: Kolmogorov, Andrey. 19562. Foundations of the Theory of Probability. New York: Chelsea.
  20. Midlarsky, Manus I. 1974. “Power, uncertainty, and the onset of international violence.” Journal of Conflict Resolution 18 (2): 395–431.
  21. Moore, Will H. 2001. “Evaluating Theory in Political Science.” Department of Political Science, The Florida State University, Tallahassee, Florida. August 9, 2001. Unpublished paper available online at: <https://whmooredotnet.files.wordpress.com/2014/07/e
  22. Moore, Will H., and David A. Siegel. 2013. A Mathematics Course for Political and Social Research. Princeton and Oxford: Princeton University Press.
  23. Nicholson, Michael. 1989. Formal Theories in International Relations. New York: Cambridge University Press.
  24. Salmon, Wesley C. 1980. "Probabilistic Causality." Pacific Philosophical Quarterly 61, 2: 50–74.
  25. Snyder, Glenn H., and Paul Diesing. 1977. Conflict Among Nations: Bargaining, Decisionmaking, and System Structure in International Crises. Princeton, N.J.: Princeton University Press.
  26. Suppes, Patrick. 1984. Probabilistic Metaphysics. New York-Oxford: Basil Blackwell.
  27. Taagepera, Rein. 1968. “Growth curves of empires.” General Systems: Yearbook of the Society for General Systems Research 13: 171–75.
  28. Taagepera, Rein. 1978. “Size and duration of empires: growth-decline curves, 3000 to 600 BC.” Social Science Research 7 (1): 180–96.
  29. Taagepera, Rein. 1979. “Size and duration of empires: Growth-decline curves, 600 B.C. to 600 A.D.” Social Science History 3: 115–38.
  30. Thomas, James J., and Kristin A. Cook, eds. 2005. Illuminating the Path. Los Alamitos, California: IEEE Computer Society.
  31. Wellin, Paul. 2013. Programming with Mathematica. Cambridge, UK: Cambridge University Press.
  32. Wohlstetter, Albert. 1959. “The delicate balance of terror.” Foreign Affairs 37 (1): 211–34.
  33. Wohlstetter, Albert. 1968. “Theory and opposed-systems design.” Journal of Conflict Resolution 12 (3): 302–31.
  34. Wright, Quincy. 1942. A Study of War, Vol. II. Chicago: University of Chicago Press.
PDF
  • Publication Year: 2022
  • Pages: 31-53
  • Content License: CC BY 4.0
  • © 2022 Author(s)

XML
  • Publication Year: 2022
  • Content License: CC BY 4.0
  • © 2022 Author(s)

Chapter Information

Chapter Title

Nabladot Analysis of Hybrid Theories in International Relations

Authors

Claudio Cioffi-Revilla

Language

English

DOI

10.36253/978-88-5518-595-0.04

Peer Reviewed

Publication Year

2022

Copyright Information

© 2022 Author(s)

Content License

CC BY 4.0

Metadata License

CC0 1.0

Bibliographic Information

Book Title

Eirene e Atena

Book Subtitle

Studi di politica internazionale in onore di Umberto Gori

Editors

Fulvio Attinà, Luciano Bozzo, Marco Cesa, Sonia Lucarelli

Peer Reviewed

Number of Pages

208

Publication Year

2022

Copyright Information

© 2022 Author(s)

Content License

CC BY 4.0

Metadata License

CC0 1.0

Publisher Name

Firenze University Press

DOI

10.36253/978-88-5518-595-0

ISBN Print

978-88-5518-594-3

eISBN (pdf)

978-88-5518-595-0

Series Title

Studi e saggi

Series ISSN

2704-6478

Series E-ISSN

2704-5919

308

Fulltext
downloads

209

Views

Export Citation

1,346

Open Access Books

in the Catalogue

2,262

Book Chapters

3,790,127

Fulltext
downloads

4,420

Authors

from 923 Research Institutions

of 65 Nations

65

scientific boards

from 348 Research Institutions

of 43 Nations

1,248

Referees

from 381 Research Institutions

of 38 Nations