Journal of Philosophical Logic

, Volume 35, Issue 2, pp 147–178 | Cite as

Socratic Proofs for Quantifiers

  • Andrzej Wiśniewski
  • Vasilyi Shangin
Short Article


First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given.


Atomic Formula Sequent Calculus Classical Propositional Logic Admissible Partition Inferential Rule 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Avron, A. (1996): The method of hypersequents in the proof theory of propositional non-classical logics, in W. Hodges et al. (eds.), Logic: Foundations to Applications, Oxford Science Publications, Clarendon, Oxford, pp. 1–32.Google Scholar
  2. Harrah, D. (2002): The logic of questions', in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Volume 8, 2nd edn, Kluwer, Dordrecht/Boston/London, pp. 1–60.Google Scholar
  3. Leszczyńska, D. (2004): Socratic proofs for some normal modal propositional logics, Log. Anal. 185–188, 259–285.Google Scholar
  4. Rasiowa, H. and Sikorski, R. (1960): On the Gentzen theorem, Fundam. Math. 48, 58–69.Google Scholar
  5. Shoesmith, D. J. and Smiley, T. J.: 1978, Multiple-Conclusion Logic, Cambridge University Press, Cambridge.Google Scholar
  6. Smullyan, R. (1968): First-Order Logic, Springer, Berlin Heidelberg New York.Google Scholar
  7. Vanackere, G. (2004): Logica en het waardevolle in de wereld. De rol van adaptieve logica's bij de constructie van theorieën (Logic and the valuable aspects of the world. The role of adaptive logics in the construction of theories). Ph.D. Dissertation, University of Ghent.Google Scholar
  8. Wiśniewski, A. (1994): Erotetic implications. J. Philos. Logic 23(2), 173–195.CrossRefGoogle Scholar
  9. Wiśniewski, A. (1995): The Posing of Questions: Logical Foundations of Erotetic Inferences, Kluwer, Dordrecht/Boston/London.Google Scholar
  10. Wiśniewski, A. (1996): The logic of questions as a theory of erotetic arguments. Synthese 109(2), 1–25.CrossRefGoogle Scholar
  11. Wiśniewski, A. (2001): Questions and inferences, Log. Anal. 173–175, 5–43.Google Scholar
  12. Wiśniewski, A. (2004): Socratic proofs, J. Philos. Logic 33, 299–326.CrossRefGoogle Scholar
  13. Wiśniewski, A., Vanackere, G. and Leszczyńska, D. (2005): Socratic proofs and paraconsistency: a case study, Stud. Log. 80, 433–468.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Section of Logic and Cognitive Science, Institute of PsychologyAdam Mickiewicz UniversityPoznańPoland
  2. 2.Department of Logic, Philosophy FacultyMoscow State UniversityMoscowRussia

Personalised recommendations