, Volume 192, Issue 6, pp 1609–1642 | Cite as

The interrogative model of inquiry meets dynamic epistemic logics

  • Yacin HamamiEmail author


The Interrogative Model of Inquiry (IMI) and Dynamic Epistemic Logics (DELs) are two central paradigms in formal epistemology. This paper is motivated by the observation of a significant complementarity between them: on the one hand, the IMI provides a framework for investigating inquiry represented as an idealized game between an Inquirer and Nature, along with an account of the interaction between questions and inferences in information-seeking processes, but is lacking a formulation in the multi-agent case; on the other hand, DELs model various operations of information change in multi-agent systems, but the field is lacking a proper integration of question and inference dynamics, along with an application to the investigation of inquiry processes. The goal of this paper is to integrate the two paradigms in such a way as to combine their respective insights. To this end, we develop a formal system called DEL\(_\mathrm{IMI }\) which aims to represent the interaction between question and inference dynamics in inquiry—as described by the IMI—in a multi-agent setting, and this in such a way as to enable an investigation of inquiry games with multi-agent dimensions. The DEL\(_\mathrm{IMI }\) system is designed to represent the possible moves of such inquiry games through three types of epistemic actions: agents addressing questions to Nature, agents addressing questions to other agents, agents drawing logical inferences. We then show how the resulting framework can be used to formally define multi-agent inquiry games. We conclude by evaluating the interest of the DEL\(_\mathrm{IMI }\) system for the IMI and DELs paradigms.


Interrogative model of inquiry Dynamic epistemic logics  Question Inference Multi-agent inquiry games 



I am very grateful to Johan van Benthem for his many advices and comments on this paper. I have benefited from discussions of earlier versions of this work with Can Başkent, Emmanuel Genot, Eric Pacuit, Ştefan Minică, Gabriel Sandu and Fernando Velázquez-Quesada. Finally, I am indebted to two anonymous reviewers for suggesting substantial improvements in the orientation and motivations of an earlier version of this paper.


  1. Ågotnes, T., van Benthem, J., van Ditmarsch, H., & Minica, S. (2011). Question–answer games. Journal of Applied Non-Classical Logics, 21(3–4), 265–288.CrossRefGoogle Scholar
  2. Ågotnes, T., & van Ditmarsch, H. (2011). What will they say? Public announcement games. Synthese, 179(1), 57–85.CrossRefGoogle Scholar
  3. Artemov, S. (2008). The logic of justification. The Review of Symbolic Logic, 1(4), 477–513.CrossRefGoogle Scholar
  4. Blackburn, P., De Rijke, M., & Venema, Y. (2002). Modal logic. Cambridge: Cambridge University Press.Google Scholar
  5. Ciardelli, I., & Roelofsen, F. (2011). Inquisitive logic. Journal of Philosophical Logic, 40(1), 55–94.CrossRefGoogle Scholar
  6. Ciardelli, I., & Roelofsen, F. (2013). Inquisitive dynamic epistemic logic. Synthese. doi: 10.1007/s11229-014-0404-7.
  7. D’Agostino, M. (1999). Tableau methods for classical propositional logic. In M. D’Agostino, D. Gabbay, R. Haehnle, & J. Posegga (Eds.), Handbook of tableau methods (pp. 45–123). Dordrecht: Kluwer.CrossRefGoogle Scholar
  8. Duc, H. (1997). Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation, 7(5), 633–648.CrossRefGoogle Scholar
  9. Enqvist, S. (2009). Interrogative belief revision in modal logic. Journal of Philosophical Logic, 38(5), 527–548.CrossRefGoogle Scholar
  10. Fagin, R., & Halpern, J. (1988). Belief, awareness, and limited reasoning. Artificial Intelligence, 34(1), 39–76.CrossRefGoogle Scholar
  11. Genot, E. (2009). The game of inquiry: The interrogative approach to inquiry and belief revision theory. Synthese, 171(2), 271–289.CrossRefGoogle Scholar
  12. Groenendijk, J., & Roelofsen, F. (2009). Inquisitive semantics and pragmatics. In J. M. Larrazabal & L. Zubeldia (Eds.), Meaning, content, and argument: Proceedings of the ILCLI international workshop on semantics, pragmatics, and rhetoric. Sebastian: University of the Basque Country Press.Google Scholar
  13. Groenendijk, J., & Stokhof, M. (1984). Studies on the semantics of questions and the pragmatics of answers. PhD thesis, Universiteit van Amsterdam.Google Scholar
  14. Groenendijk, J., & Stokhof, M. (1997). Questions. In J. van Benthem & A. ter Meulen (Eds.), Handbook of logic and language (pp. 1055–1124). Amsterdam: Elsevier.CrossRefGoogle Scholar
  15. Grossi, D., & Velázquez-Quesada, F. (2009). Twelve angry men: A study on the fine-grain of announcements. In X. He, J. Horty, & E. Pacuit (Eds.), Logic, rationality, and interaction. LNCS (Vol. 5834, pp. 147–160). New York: Springer.Google Scholar
  16. Halonen, I., & Hintikka, J. (2005). Toward a theory of the process of explanation. Synthese, 143(1), 5–61.CrossRefGoogle Scholar
  17. Halpern, J. Y., & Pucella, R. (2011). Dealing with logical omniscience: Expressiveness and pragmatics. Artificial Intelligence, 175(1), 220–235.CrossRefGoogle Scholar
  18. Hintikka, J. (1976). The semantics of questions and the questions of semantics: Case studies in the interrelations of logic, semantics, and syntax. Acta Philosophica Fennica, 28(4).Google Scholar
  19. Hintikka, J. (1985). A spectrum of logics of questioning in recent developments in dialogue logics. Philosophica, 35(1), 135–150.Google Scholar
  20. Hintikka, J. (1988). What is the logic of experimental inquiry? Synthese, 74(2), 173–190.CrossRefGoogle Scholar
  21. Hintikka, J. (1992). The interrogative model of inquiry as a general theory of argumentation. Communication and Cognition, 25(2–3), 221–242.Google Scholar
  22. Hintikka, J. (1999). Inquiry as inquiry: A logic of scientific discovery, Jaakko Hintikka selected papers (Vol. 5). Dordrecht: Kluwer.Google Scholar
  23. Hintikka, J. (2007). Socratic epistemology: Explorations of knowledge-seeking by questioning. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  24. Hintikka, J., Halonen, I., & Mutanen, A. (1999). Interrogative logic as a general theory of reasoning. In Inquiry as inquiry: A logic of scientific discovery (pp. 47–90). Dordrecht: Kluwer.Google Scholar
  25. Jago, M. (2009). Epistemic logic for rule-based agents. Journal of Logic, Language and Information, 18(1), 131–158.CrossRefGoogle Scholar
  26. Longino, H. (2013). The social dimensions of scientific knowledge. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy.
  27. Peliš, M., & Majer, O. (2009). Logic of questions from the viewpoint of dynamic epistemic logic. In M. Peliš (Ed.), The Logica Yearbook (2009) (pp. 157–172). London: College Publications.Google Scholar
  28. Peliš, M., & Majer, O. (2011). Logic of questions and public announcements. In N. Bezhanishvili, S. Löbner, K. Schwabe, & L. Spada (Eds.), Eighth international Tbilisi symposium on logic, language and computation (2009). Lecture notes in computer science (pp. 145–157). Berlin: Springer.Google Scholar
  29. Pucella, R. (2006). Deductive algorithmic knowledge. Journal of Logic and Computation, 16(2), 287–309.CrossRefGoogle Scholar
  30. Roelofsen, F. (2013). Algebraic foundations for the semantic treatment of inquisitive content. Synthese, 190(1), 79–102.Google Scholar
  31. van Benthem, J. (2008). Merging observation and access in dynamic logic. Journal of Logic Studies, 1(1), 1–17.Google Scholar
  32. van Benthem, J. (2011). Logical dynamics of information and interaction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  33. van Benthem, J. (2013). Logic in games. Cambridge, MA: MIT Press.Google Scholar
  34. van Benthem, J., & Minică, Ş. (2012). Toward a dynamic logic of questions. Journal of Philosophical Logic, 41(4), 633–669.CrossRefGoogle Scholar
  35. van Benthem, J., & Velázquez-Quesada, F. (2010). The dynamics of awareness. Synthese, 177, 5–27.CrossRefGoogle Scholar
  36. van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemic Logic. Synthese Library (Vol. 337). Heidelberg: Springer.Google Scholar
  37. Velázquez-Quesada, F. (2009). Inference and update. Synthese (Knowledge, Rationality and Action), 169(2), 283–300.Google Scholar
  38. Velázquez-Quesada, F. R. (2010). Dynamic epistemic logic for implicit and explicit beliefs. In O. Boissier, A. E. F. Seghrouchni, S. Hassas, & N. Maudet (Eds.), MALLOW 2010, CEUR workshop proceedings (Vol. 627), Lyon, France.
  39. Velázquez-Quesada, F. (2011). Small steps in dynamics of information. PhD Thesis, Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam (UvA), Amsterdam.Google Scholar
  40. Wiśniewski, A. (2001). Questions and inferences. Logique & Analyse, 173–175, 5–43.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of Science, Vrije Universiteit BrusselBrusselsBelgium

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