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Alexander Belikov
Moscow State University
  1.  2
    The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins.Yaroslav Shramko, Dmitry Zaitsev & Alexander Belikov - 2019 - Journal of Philosophical Logic 48 (5):787-808.
    In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the (...)
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  2.  15
    First-Degree Entailment and its Relatives.Yaroslav Shramko, Dmitry Zaitsev & Alexander Belikov - 2017 - Studia Logica 105 (6):1291-1317.
    We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \, where both \ and \ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left of the turnstile. In this way, it is possible (...)
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    The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins.Yaroslav Shramko, Dmitry Zaitsev & Alexander Belikov - 2019 - Journal of Philosophical Logic 48 (5):787-808.
    In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the (...)
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