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The Method of Socratic Proofs Meets Correspondence Analysis

Dorota Leszczyńska-Jasion;  Yaroslav Petrukhin;  Vasilyi Shangin — 2019

Bulletin of the Section of Logic

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...

Functional Completeness in CPL via Correspondence Analysis

Dorota Leszczyńska-Jasion;  Yaroslav Petrukhin;  Vasilyi Shangin;  Marcin Jukiewicz — 2019

Bulletin of the Section of Logic

Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set (sets) of rules characterizing a two-argument Boolean function(s) to the negation fragment of classical propositional logic. The...

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