Arguably Argumentative: A Formal Approach to the Argumentative Theory of Reason

  • Sjur K. DyrkolbotnEmail author
  • Truls Pedersen
Part of the Synthese Library book series (SYLI, volume 376)


We propose a formal approach to the argumentative theory of reason, combining argumentation theory and modal logic in a novel way. We show that the resulting framework can be used to model important mechanisms identified by the theory, including how confirmation bias and other problematic modes of reasoning may in fact serve an important argumentative purpose that can give rise to classically sound conclusions through the process of social deliberation. We go on to suggest that the argumentative theory is based on an understanding of intelligent reasoning and rationality that sees these notions as irreducibly social, and that the argumentative theory itself provides a possible starting point in the search for new theoretical foundations based on this understanding. Moreover, we suggest that formal logic can aid in the investigation of foundational issues, and we sketch the development of an axiomatic approach to the study of rational deliberation.


Rationality Argumentation Deliberation Cognitive bias Modal logic 


  1. Ågotnes, T., & van Ditmarsch, H. P. (2011). What will they say? Public announcement games. Synthese, 179(Supplement-1), 57–85.Google Scholar
  2. Alur R., Henzinger T. A., & Kupferman, O. (2002). Alternating-time temporal logic. Journal of the ACM, 49(5), 672–713.CrossRefGoogle Scholar
  3. Arieli, O., & Caminada, M. W. A. (2013). A QBF-based formalization of abstract argumentation semantics. Journal of Applied Logic, 11(2), 229–252.CrossRefGoogle Scholar
  4. Baroni, P., & Giacomin, M. (2007). On principle-based evaluation of extension-based argumentation semantics. Artificial Intelligence, 171(1015), 675–700.CrossRefGoogle Scholar
  5. Bezem, M., Grabmayer C., & Walicki, M. (2012). Expressive power of digraph solvability. Annals of Pure and Applied Logic, 162(3), 200–213.CrossRefGoogle Scholar
  6. Blume, L., & Durlauf, S. (2001). The interaction-based approach to socioeconomic behavior. In S. Durlauf & P. Young (Eds.), Social dynamics. Washington, DC: Brookings Institutions Press.Google Scholar
  7. Brewka, G., Dunne, P. E., & Woltran, S. (2011). Relating the semantics of abstract dialectical frameworks and standard AFs. In T. Walsh (Ed.), IJCAI, Barcelona (pp. 780–785). IJCAI/AAAI.Google Scholar
  8. Brewka, G., & Gordon, T. F. (2010). Carneades and abstract dialectical frameworks: A reconstruction. In Proceedings of the 2010 Conference on Computational Models of Argument: Proceedings of COMMA 2010 (pp. 3–12). Amsterdam: IOS Press.Google Scholar
  9. Broersen, J. (2011). Making a start with the stit logic analysis of intentional action. Journal of Philosophical Logic, 40(4), 499–530.CrossRefGoogle Scholar
  10. Caminada, M. W. A., & Gabbay D. M. (2009). A logical account of formal argumentation. Studia Logica, 93(2–3), 109–145.CrossRefGoogle Scholar
  11. Coste-Marquis, S., Devred, C., Konieczny S., Lagasquie-Schiex, M.-C., & Marquis, P. (2007). On the merging of Dung’s argumentation systems. Artificial Intelligence, 171(10–15), 730–753.CrossRefGoogle Scholar
  12. Dung, P. M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77, 321–357.CrossRefGoogle Scholar
  13. Dunne, P. E., Marquis, P., & Wooldridge, M. (2012). Argument aggregation: Basic axioms and complexity results. In B. Verheij, S. Szeider, & S. Woltran (Eds.), COMMA (Vol. 245, pp. 129–140). Vienna: IOS Press.Google Scholar
  14. Dyrkolbotn, S. (2013). The same, similar, or just completely different? Equivalence for argumentation in light of logic. In L. Libkin, U. Kohlenbach, & R. Queiroz (Eds.), Logic, language information, and computation (Vol. 8071, pp. 96–110). Berlin/Heidelberg: Springer.Google Scholar
  15. Dyrkolbotn, S., & Walicki, M. (2014). Propositional discourse logic. Synthese, 191(5), 863–899.CrossRefGoogle Scholar
  16. Gabbay D. M., & Rodrigues, O. (2014). An equational approach to the merging of argumentation networks. Journal of Logic and Computation, 24(6), 1253–1277.CrossRefGoogle Scholar
  17. Galeana-Sánchez, H., & Neumann-Lara, V. (1984). On kernels and semikernels of digraphs. Discrete Mathematics, 48(1), 67–76.CrossRefGoogle Scholar
  18. Grossi, D. (2010). On the logic of argumentation theory. In Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: Volume 1 – Volume 1 (pp. 409–416). Richland: International Foundation for Autonomous Agents and Multiagent Systems.Google Scholar
  19. Hoek, W., Roberts, M., & Wooldridge, M. (2007). Social laws in alternating time: Effectiveness, feasibility, and synthesis. Synthese, 156(1), 1–19.CrossRefGoogle Scholar
  20. Kock, C. (2007). Norms of legitimate dissensus. Informal Logic, 27(2), 179–196.Google Scholar
  21. Kock, C. (2009). Choice is not true or false: The domain of rhetorical argumentation. Argumentation, 23(1), 61–80.CrossRefGoogle Scholar
  22. List, C., & Dryzek, J. (2003). Social choice theory and deliberative democracy: A reconciliation. British Journal of Political Science, 33(1), 1–28.CrossRefGoogle Scholar
  23. Mead, G. H. (1967). Mind, self and society (3rd ed.). Chicago: University of Chicago Press.CrossRefGoogle Scholar
  24. Mercier H., & Sperber D. (2011). Why do humans reason? Arguments for an argumentative theory. Behavioral and Brain Sciences, 34(02), 57–74.CrossRefGoogle Scholar
  25. Ossowski, S. (Ed.). (2013). Agreement technologies (Vol. 8). Dordrecht: Springer.Google Scholar
  26. Parikh, R. (2002). Social software. Synthese, 132(3), 187–211.CrossRefGoogle Scholar
  27. Rahwan, I., & Simari, G. R. (Eds.). (2009). Argumentation in artificial intelligence. Dordrecht/New York: Springer.Google Scholar
  28. Richardson, M. (1953). Solutions of irreflexive relations. The Annals of Mathematics, Second Series, 58(3), 573–590.CrossRefGoogle Scholar
  29. Russell, S. J. (1997). Rationality and intelligence. Artificial Intelligence, 94(1–2), 57–77.CrossRefGoogle Scholar
  30. Stenning, K., & van Lambalgen, M. (2005). Semantic interpretation as computation in nonmonotonic logic: The real meaning of the suppression task. Cognitive Science, 29(6), 919–960.CrossRefGoogle Scholar
  31. Stenning, K., & van Lambalgen, M. (2008). Human reasoning and cognitive science. Cambridge: MIT Press.Google Scholar
  32. Terrell, T. P. (2012). The art of legal reasoning and the angst of judging: Of balls, strikes, and moments of truth. Northwestern Journal of Law and Social Policy, 8(1), 35–88.Google Scholar
  33. Toulmin, S. (2003). The uses of argument (2nd ed.). Cambridge/New York: Cambridge University Press. (First edition from 1958).Google Scholar
  34. van Benthem, J. (2008). Logic and reasoning: Do the facts matter? Studia Logica, 88(1), 67–84.CrossRefGoogle Scholar
  35. van Benthem, J. (2011). Logical dynamics of information and interaction. Cambridge/New York: Cambridge University Press.CrossRefGoogle Scholar
  36. Verbrugge, R. (2009). Logic and social cognition: The facts matter, and so do computational models. Journal of Philosophical Logic, 38(6), 649–680.CrossRefGoogle Scholar
  37. de Waal, F. B. M., & Ferrari, P. F. (2010). Towards a bottom-up perspective on animal and human cognition. Trends in Cognitive Sciences, 14(5), 201–207.CrossRefGoogle Scholar
  38. Wohlrapp, H. (1998). A new light on non-deductive argumentation schemes. Argumentation, 12(3), 341–350.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Philosophy and Religious StudiesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Information Science and Media StudiesUniversity of BergenBergenNorway

Personalised recommendations