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Yaroslav Petrukhin [25]Yaroslav I. Petrukhin [1]
  1.  63
    Exactly true and non-falsity logics meeting infectious ones.Alex Belikov & Yaroslav Petrukhin - 2020 - Journal of Applied Non-Classical Logics 30 (2):93-122.
    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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  2.  30
    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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  3.  31
    On a multilattice analogue of a hypersequent S5 calculus.Oleg Grigoriev & Yaroslav Petrukhin - forthcoming - Logic and Logical Philosophy:1.
  4.  27
    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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  5.  45
    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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  6.  32
    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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  7.  24
    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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  8.  24
    Axiomatizing a Minimal Discussive Logic.Oleg Grigoriev, Marek Nasieniewski, Krystyna Mruczek-Nasieniewska, Yaroslav Petrukhin & Vasily Shangin - 2023 - Studia Logica 111 (5):855-895.
    In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as $$ {\textsf {D}}_{\textsf {0}}$$ D 0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2 but with the help of the deontic normal logic (...)
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  9.  28
    Automated Proof-searching for Strong Kleene Logic and its Binary Extensions via Correspondence Analysis.Yaroslav Petrukhin & Vasilyi Shangin - forthcoming - Logic and Logical Philosophy:1.
  10.  30
    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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  11.  28
    Non-transitive Correspondence Analysis.Yaroslav Petrukhin & Vasily Shangin - 2023 - Journal of Logic, Language and Information 32 (2):247-273.
    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 (...)
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  12.  26
    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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  13.  29
    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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  14.  15
    Modal multilattice logics with Tarski, Kuratowski, and Halmos operators.Oleg Grigoriev & Yaroslav Petrukhin - forthcoming - Logic and Logical Philosophy:1.
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  15.  37
    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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  16.  14
    Computer-Aided Searching for a Tabular Many-Valued Discussive Logic—Matrices.Marcin Jukiewicz, Marek Nasieniewski, Yaroslav Petrukhin & Vasily Shangin - forthcoming - Logic Journal of the IGPL.
    In the paper, we tackle the matter of non-classical logics, in particular, paraconsistent ones, for which not every formula follows in general from inconsistent premisses. Our benchmark is Jaśkowski’s logic, modeled with the help of discussion. The second key origin of this paper is the matter of being tabular, i.e. being adequately expressible by finitely many finite matrices. We analyse Jaśkowski’s non-tabular discussive (discursive) logic $ \textbf {D}_{2}$, one of the first paraconsistent logics, from the perspective of a trivalent tabular (...)
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  17.  12
    Algebraic Completeness of Connexive and Bi-Intuitionistic Multilattice Logics.Yaroslav Petrukhin - 2024 - Journal of Logic, Language and Information 33 (2):179-196.
    In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.
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  18.  21
    On Paracomplete Versions of Jaśkowski's Discussive Logic.Krystyna Mruczek-Nasieniewska, Yaroslav Petrukhin & Vasily Shangin - 2024 - Bulletin of the Section of Logic 53 (1):29-61.
    Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2p.
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  19.  4
    Uniform Cut-Free Bisequent Calculi for Three-Valued Logics.Andrzej Indrzejczak & Yaroslav Petrukhin - 2024 - Logic and Logical Philosophy 33 (3):463-506.
    We present a uniform characterisation of three-valued logics by means of a bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as the weakest kind of system in the rich family of generalised SC operating on items being some collections of ordinary sequents, like hypersequent and nested sequent calculi. It seems that for many non-classical logics, including some many-valued, paraconsistent and modal logics, (...)
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  20.  16
    (1 other version)Provability multilattice logic.Yaroslav Petrukhin - 2022 - Journal of Applied Non-Classical Logics 32 (4):239-272.
    In this paper, we introduce provability multilattice logic PMLn and multilattice arithmetic MPAn which extends first-order multilattice logic with equality by multilattice versions of Peano axioms. We show that PMLn has the provability interpretation with respect to MPAn and prove the arithmetic completeness theorem for it. We formulate PMLn in the form of a nested sequent calculus and show that cut is admissible in it. We introduce the notion of a provability multilattice and develop algebraic semantics for PMLn on its (...)
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  21.  16
    Axiomatization of non-associative generalisations of Hájek's BL and psBL.Yaroslav Petrukhin - 2020 - 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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  22.  21
    The Logic of Internal Rational Agent.Yaroslav Petrukhin - 2021 - Australasian Journal of Logic 18 (2).
    In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent textbf{LRA} cite{LRA}. We call our logic $ bf LIRA$. In contrast to textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic cite{ZS}. This logic may be useful in a situation when according to an agent's point of (...)
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