Abstract
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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Wiśniewski, A. Socratic Proofs. Journal of Philosophical Logic 33, 299–326 (2004). https://doi.org/10.1023/B:LOGI.0000031374.60945.6e
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DOI: https://doi.org/10.1023/B:LOGI.0000031374.60945.6e