Studia Logica

, Volume 106, Issue 2, pp 295–309 | Cite as

Deduction and Reduction Theorems for Inferential Erotetic Logic

  • Andrzej Wiśniewski
Open Access


The concepts of question evocation and erotetic implication play central role in Inferential Erotetic Logic. In this paper, deduction theorems for question evocation and erotetic implication are proven. Moreover, it is shown how question evocation by a finite non-empty set of declaratives can be reduced to question evocation by the empty set, and how erotetic implication based on a finite non-empty set of declaratives can be reduced to a relation between questions only.


Logic of questions Multiple-conclusion logic Deduction 


  1. 1.
    Belnap, N. D., and Th. P. Steel, The Logic of Questions and Answers, Yale University Press, New Haven, 1976.Google Scholar
  2. 2.
    Ciardelli, I., Questions in Logic, ILLC, Amsterdam, 2015.Google Scholar
  3. 3.
    Ginzburg, J., Questions: Logic and interactions, in J. van Benthem and A. ter Meulen (eds.), Handbook of Logic and Language, 2nd edn, Elsevier, Amsterdam, 2011, pp. 1133–1146.Google Scholar
  4. 4.
    Groenendijk, J., and M. Stokhof, Questions, in J. van Benthem and A. ter Meulen (eds.), Handbook of Logic and Language, 2nd edn, Elsevier, Amsterdam, 2011, pp. 1059–1132.Google Scholar
  5. 5.
    Hamami, Y., The interrogative model of inquiry meets dynamic epistemic logic. Master’s thesis, ILLC, University of Amsterdam, 2010.Google Scholar
  6. 6.
    Hamami, Y., and F. Roelofsen, guest editors. Logics of questions, Synthese 192, Issue 6, 2015.Google Scholar
  7. 7.
    Harrah, D., The logic of questions, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, vol. 8, 2nd edn, Kluwer, Dordrecht/Boston/London, 2002, pp. 1–60.Google Scholar
  8. 8.
    Hintikka, J., Semantics of Questions and the Questions of Semantics, vol. 28 of Acta Philosophica Fennica, North-Holland, Amsterdam, 1976.Google Scholar
  9. 9.
    Hintikka, J., Inquiry as Inquiry: A Logic of Scientific Discovery, Kluwer, Dordrecht/Boston/London, 1999.CrossRefGoogle Scholar
  10. 10.
    Hintikka, J., Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning, Cambridge University Press, Cambridge, 2007.CrossRefGoogle Scholar
  11. 11.
    Krifka, M., Questions, in K. von Helsinger, C. Maieborn and P. Portner (eds.), Semantics. An International Handbook of Natural Language Meaning, vol. II, Mouton de Gruyter, Berlin, 2011, pp. 1742–1785.Google Scholar
  12. 12.
    Łupkowski, P., Logic of Questions in the Wild. Inferential Erotetic Logic in Information Seeking Dialogue Modelling, College Publications, London, 2016.Google Scholar
  13. 13.
    Onea, E., Potential Questions at the Semantics-Pragmatics Interface, Brill, Leiden/Boston, 2016.CrossRefGoogle Scholar
  14. 14.
    Peliš, M., Inferences with Ignorance: Logics of Questions. Inferential Erotetic Logic & Erotetic Epistemic Logic, Karolinum Press, Prague, 2016.Google Scholar
  15. 15.
    Shoesmith, D. J., and T. J. Smiley, Multiple-conclusion Logic, Cambridge University Press, Cambridge, 1978.Google Scholar
  16. 16.
    Skura, T., and A. Wiśniewski, A system for proper multiple-conclusion entailment, Logic and Logical Philosophy 24:241–253, 2015.Google Scholar
  17. 17.
    van Benthem, J., Logical Dynamics of Information and Interaction, Cambridge University Press, Cambridge, 2011.CrossRefGoogle Scholar
  18. 18.
    Wiśniewski, A., The Posing of Questions: Logical Foundations of Erotetic Inferences, Kluwer, Dordrecht/Boston/London, 1995.CrossRefGoogle Scholar
  19. 19.
    Wiśniewski, A., Questions, Inferences, and Scenarios, College Publications, London, 2013.Google Scholar
  20. 20.
    Wiśniewski, A., Semantics of questions, in S. Lappin and Ch. Fox (eds.), The Handbook of Contemporary Semantic Theory, 2nd edn, Wiley-Blackwell, Oxford, 2015, pp. 273–313.Google Scholar
  21. 21.
    Wiśniewski, A., An axiomatic account of question evocation. The propositional case, Axioms 5(2):14, 2016.CrossRefGoogle Scholar
  22. 22.
    Wiśniewski, A., and D. Leszczyńska-Jasion, Inferential erotetic logic meets inquisitive semantics, Synthese 192:1585–1608, 2015.Google Scholar
  23. 23.
    Wójcicki, R., Lectures on Propositional Calculi, Ossolineum, Wrocław, 1984.Google Scholar
  24. 24.
    Wójcicki, R., Theory of Logical Calculi. Basic Theory of Consequence Operations, Kluwer, Dordrecht/Boston/London, 1988.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Logic and Cognitive Science Institute of PsychologyAdam Mickiewicz UniversityPoznańPoland

Personalised recommendations