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Journal of Philosophical Logic

, Volume 33, Issue 3, pp 299–326 | Cite as

Socratic Proofs

  • Andrzej Wiśniewski
Article

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.

logic of questions proof search sequent calculi 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Andrzej Wiśniewski
    • 1
  1. 1.Institute of Philosophy University of Zielona Góra Wojska PolskiegoZielona GóraPoland

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