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Yaroslav Petrukhin [14]Yaroslav I. Petrukhin [1]
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Yaroslav Petrukhin
Moscow State University
Yaroslav Petrukhin
Moscow State University
  1.  5
    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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  2.  10
    Exactly True and Non-Falsity Logics Meeting Infectious Ones.Alex Belikov & Yaroslav Petrukhin - forthcoming - Journal of Applied Non-Classical Logics:1-29.
    In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding ‘exactly true’ and ‘non-falsity’ versions of four-valued logics that emerged in series of recent works [Pietz & Rivieccio (2013). Nothing but the truth. Journal of Philosophical Logic, 42(1), 125–135; Shramko (2019). Dual-Belnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413–433; Shramko et al. (2017). First-degree entailment and its relatives. Studia Logica, 105(6), 1291–1317] to the case (...)
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  3.  10
    Natural Deduction for Post’s Logics and Their Duals.Yaroslav Petrukhin - 2018 - Logica Universalis 12 (1-2):83-100.
    In this paper, we introduce the notion of dual Post’s negation and an infinite class of Dual Post’s finitely-valued logics which differ from Post’s ones with respect to the definitions of negation and the sets of designated truth values. We present adequate natural deduction systems for all Post’s k-valued ) logics as well as for all Dual Post’s k-valued logics.
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  4.  15
    Natural Deduction for Fitting’s Four-Valued Generalizations of Kleene’s Logics.Yaroslav I. Petrukhin - 2017 - Logica Universalis 11 (4):525-532.
    In this paper, we present sound and complete natural deduction systems for Fitting’s four-valued generalizations of Kleene’s three-valued regular logics.
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  5.  12
    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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  6.  8
    Two Proofs of the Algebraic Completeness Theorem for Multilattice Logic.Oleg Grigoriev & Yaroslav Petrukhin - 2019 - Journal of Applied Non-Classical Logics 29 (4):358-381.
    Shramko [. Truth, falsehood, information and beyond: The American plan generalized. In K. Bimbo, J. Michael Dunn on information based logics, outstanding contributions to logic...
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  7.  5
    On a Multilattice Analogue of a Hypersequent S5 Calculus.Oleg Grigoriev & Yaroslav Petrukhin - forthcoming - Logic and Logical Philosophy:1.
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  8.  10
    Generalized Correspondence Analysis for Three-Valued Logics.Yaroslav Petrukhin - 2018 - Logica Universalis 12 (3-4):423-460.
    Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP -language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete (...)
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  9.  15
    Simplified Kripke-Style Semantics for Some Normal Modal Logics.Andrzej Pietruszczak, Mateusz Klonowski & Yaroslav Petrukhin - 2020 - Studia Logica 108 (3):451-476.
    Pietruszczak :163–171, 2009. https://doi.org/10.12775/LLP.2009.013) proved that the normal logics \, \ ), \ are determined by suitable classes of simplified Kripke frames of the form \, where \. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of \. Furthermore, a modal logic is a normal extension of \ ; \; \) if and only if it is (...)
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  10.  7
    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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  11.  8
    On Vidal's Trivalent Explanations for Defective Conditional in Mathematics.Yaroslav Petrukhin & Vasily Shangin - 2018 - 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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  12.  1
    Axiomatization of Non-Associative Generalisations of Hájek's BL and psBL.Yaroslav Petrukhin - 2019 - Journal of Applied Non-Classical Logics 30 (1):1-15.
    ABSTRACTIn this paper, we consider non-associative generalisations of Hájek's logics BL and psBL. As it was shown by Cignoli, Esteva, Godo, and Torrens, the former is the logic of continuous t-norms and their residua. Botur introduced logic naBL which is the logic of non-associative continuous t-norms and their residua. Thus, naBL can be viewed as a non-associative generalisation of BL. However, Botur has not presented axiomatization of naBL. We fill this gap by constructing an adequate Hilbert-style calculus for naBL. Although, (...)
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  13.  18
    Automated Correspondence Analysis for the Binary Extensions of the Logic of Paradox.Yaroslav Petrukhin & Vasily Shangin - 2017 - Review of Symbolic Logic 10 (4):756-781.
    B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.
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