Socratic proofs

Journal of Philosophical Logic 33 (3):299-326 (2004)
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Our aim is to express in exact terms the old idea of solving problems by pure questioning. We consider the problem of derivability: "Is A derivable from Δ by classical propositional logic?". We develop a calculus of questions E*; a proof (called a Socratic proof) is a sequence of questions ending with a question whose affirmative answer is, in a sense, evident. The calculus is sound and complete with respect to classical propositional logic. A Socratic proof in E* can be transformed into a Gentzen-style proof in some sequent calculi. Next we develop a calculus of questions E**; Socratic proofs in E** can be transformed into analytic tableaux. We show that Socratic proofs can be grounded in Inferential Erotetic Logic. After a slight modification, the analyzed systems can also be viewed as hypersequent calculi.



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Andrzej Wiśniewski
Adam Mickiewicz University

References found in this work

First-Order Logic.Raymond Merrill Smullyan - 1968 - Berlin, Germany: New York [Etc.]Springer-Verlag.
Multiple Conclusion Logic.D. J. Shoesmith & Timothy Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
The Posing of Questions: Logical Foundations of Erotetic Inferences.Andrzej Wiśniewski - 1995 - Dordrecht and Boston: Kluwer Academic Publishers.
The method of hypersequents in the proof theory of propositional non-classical logics.Arnon Avron - 1996 - In Wilfrid Hodges (ed.), Logic: Foundations to Applications. Oxford: pp. 1-32.

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