Geodesic
The Method of Socratic Proofs Meets Correspondence Analysis
Bulletin of the Section of Logic, Tome 48 (2019) no. 2, pp. 99-116

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The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions.
Keywords: Socratic proofs, correspondence analysis, invertible rule, inferential erotetic logic, classical propositional logic, sequent calculus 
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Leszczyńska-Jasion, Dorota; Petrukhin, Yaroslav; Shangin, Vasilyi. The Method of Socratic Proofs Meets Correspondence Analysis. Bulletin of the Section of Logic, Tome 48 (2019) no. 2, pp. 99-116. http://geodesic.mathdoc.fr/item/BSL_2019_48_2_a1/