Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
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.
Leszczyńska, D. (2004): Socratic proofs for some normal modal propositional logics, Log. Anal. 185–188, 259–285.
Rasiowa, H. and Sikorski, R. (1960): On the Gentzen theorem, Fundam. Math. 48, 58–69.
Shoesmith, D. J. and Smiley, T. J.: 1978, Multiple-Conclusion Logic, Cambridge University Press, Cambridge.
Smullyan, R. (1968): First-Order Logic, Springer, Berlin Heidelberg New York.
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.
Wiśniewski, A. (1994): Erotetic implications. J. Philos. Logic 23(2), 173–195.
Wiśniewski, A. (1995): The Posing of Questions: Logical Foundations of Erotetic Inferences, Kluwer, Dordrecht/Boston/London.
Wiśniewski, A. (1996): The logic of questions as a theory of erotetic arguments. Synthese 109(2), 1–25.
Wiśniewski, A. (2001): Questions and inferences, Log. Anal. 173–175, 5–43.
Wiśniewski, A. (2004): Socratic proofs, J. Philos. Logic 33, 299–326.
Wiśniewski, A., Vanackere, G. and Leszczyńska, D. (2005): Socratic proofs and paraconsistency: a case study, Stud. Log. 80, 433–468.
Author information
Authors and Affiliations
Corresponding author
Additional information
*Research for this paper was supported by The Foundation for Polish Science (both authors), and indirectly (in the case of the first author) by a bilateral exchange project funded by the Ministry of the Flemish Community (project BIL 01/80) and the State Committee for Scientific Research, Poland.
Rights and permissions
About this article
Cite this article
Wiśniewski, A., Shangin, V. Socratic Proofs for Quantifiers★ . J Philos Logic 35, 147–178 (2006). https://doi.org/10.1007/s10992-005-9000-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-005-9000-0