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The Method of Socratic Proofs Meets Correspondence Analysis

Dorota Leszczyńska-Jasion, Yaroslav Petrukhin & Vasilyi Shangin

Bulletin of the Section of Logic 48 (2):99-116 (2019)

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Non-transitive Correspondence Analysis.Yaroslav Petrukhin & Vasily Shangin - 2023 - Journal of Logic, Language and Information 32 (2):247-273.details The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent logic (...) Download Export citation Bookmark 1 citation
Correspondence Analysis for Some Fragments of Classical Propositional Logic.Yaroslav Petrukhin & Vasilyi Shangin - 2021 - Logica Universalis 15 (1):67-85.details In the paper, we apply Kooi and Tamminga’s correspondence analysis to some conventional and functionally incomplete fragments of classical propositional logic. In particular, the paper deals with the implication, disjunction, and negation fragments. Additionally, we consider an application of correspondence analysis to some connectiveless fragment with certain basic properties of the logical consequence relation only. As a result of the application, one obtains a sound and complete natural deduction system for any binary extension of each fragment in question. With the (...) Download Export citation Bookmark 2 citations

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