Socratic Trees

Studia Logica 101 (5):959-986 (2013)
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Abstract

The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction.

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Andrzej Wiśniewski
Adam Mickiewicz University

References found in this work

First-order logic.Raymond Merrill Smullyan - 1968 - New York [etc.]: Springer Verlag.
Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
The Posing of Questions: Logical Foundations of Erotetic Inferences.Andrzej Wiśniewski - 1995 - Dordrecht and Boston: Kluwer Academic Publishers.
First-order Logic.William Craig - 1975 - Journal of Symbolic Logic 40 (2):237-238.

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