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Vasilyi Shangin [6]Vasily Shangin [3]
  1.  37
    Socratic Proofs for Quantifiers★.Andrzej Wiśniewski & Vasilyi Shangin - 2006 - Journal of Philosophical Logic 35 (2):147-178.
    First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given.
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  2.  7
    Automated Proof-Searching for Strong Kleene Logic and its Binary Extensions Via Correspondence Analysis.Yaroslav Petrukhin & Vasilyi Shangin - forthcoming - Logic and Logical Philosophy:1.
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  3.  14
    Functional Completeness in CPL Via Correspondence Analysis.Dorota Leszczyńska-Jasion, Yaroslav Petrukhin, Vasilyi Shangin & Marcin Jukiewicz - 2019 - Bulletin of the Section of Logic 48 (1).
    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 of rules characterizing a two-argument Boolean function to the negation fragment of classical propositional logic. The properties of soundness and completeness (...)
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  4.  10
    Natural Deduction System in Paraconsistent Setting: Proof Search for PCont.Vasilyi Shangin & Alexander Bolotov - 2012 - Journal of Intelligent Systems 21 (1):1-24.
    . This paper continues a systematic approach to build natural deduction calculi and corresponding proof procedures for non-classical logics. Our attention is now paid to the framework of paraconsistent logics. These logics are used, in particular, for reasoning about systems where paradoxes do not lead to the `deductive explosion', i.e., where formulae of the type `A follows from false', for any A, are not valid. We formulate the natural deduction system for the logic PCont, explain its main concepts, define a (...)
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  5.  7
    Correspondence Analysis for Some Fragments of Classical Propositional Logic.Yaroslav Petrukhin & Vasilyi Shangin - 2021 - Logica Universalis 15 (1):67-85.
    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 (...)
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  6.  10
    The Method of Socratic Proofs Meets Correspondence Analysis.Dorota Leszczyńska-Jasion, Yaroslav Petrukhin & Vasilyi Shangin - 2019 - Bulletin of the Section of Logic 48 (2):99-116.
    The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic 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. (...)
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  7.  12
    On Vidal's Trivalent Explanations for Defective Conditional in Mathematics.Yaroslav Petrukhin & Vasily Shangin - 2019 - Journal of Applied Non-Classical Logics 29 (1):64-77.
    ABSTRACTThe paper deals with a problem posed by Mathieu Vidal to provide a formal representation for defective conditional in mathematics Vidal, M. [. The defective conditional in mathematics. Journal of Applied Non-Classical Logics, 24, 169–179]. The key feature of defective conditional is that its truth-value is indeterminate if its antecedent is false. In particular, we are interested in two explanations given by Vidal with the use of trivalent logics. By analysing a simple argument from plane geometry, where defective conditional is (...)
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  8.  2
    Non-transitive Correspondence Analysis.Yaroslav Petrukhin & Vasily Shangin - forthcoming - Journal of Logic, Language and Information:1-27.
    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 \. As a result, for each binary extension of \, 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 (...)
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