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Alex Citkin [7]Alexander Citkin [2]
  1.  3
    Admissibility in Positive Logics.Alex Citkin - 2017 - Logica Universalis 11 (4):421-437.
    The paper studies admissibility of multiple-conclusion rules in positive logics. Using modification of a method employed by M. Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility of multiple-conclusion rules in the positive logics is equivalent to the problem of admissibility in intermediate logics defined by positive additional axioms. Moreover, a multiple-conclusion rule \ follows from a set of multiple-conclusion rules \ over a positive logic \ if and only if \ follows from (...)
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  2.  1
    Characteristic Inference Rules.Alex Citkin - 2015 - Logica Universalis 9 (1):27-46.
    The goal of this paper is to generalize a notion of quasi-characteristic inference rule in the following way: with every finite partial algebra we associate a rule, and study the properties of these rules. We prove that any equivalential logic can be axiomatized by such rules. We further discuss the correlations between characteristic rules of the finite partial algebras and canonical rules. Then, with every algebra we associate a set of characteristic rules that correspond to each finite partial subalgebra of (...)
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  3.  9
    A Note on Admissible Rules and the Disjunction Property in Intermediate Logics.Alexander Citkin - 2012 - Archive for Mathematical Logic 51 (1-2):1-14.
    With any structural inference rule A/B, we associate the rule ${(A \lor p)/(B \lor p)}$ , providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( ${\lor}$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a ${\lor}$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the ${\lor}$ -extension of each admissible rule is admissible. We prove (...)
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  4.  7
    Algebraic Logic Perspective on Prucnal’s Substitution.Alex Citkin - 2016 - Notre Dame Journal of Formal Logic 57 (4):503-521.
    A term td is called a ternary deductive term for a variety of algebras V if the identity td≈r holds in V and ∈θ yields td≈td for any A∈V and any principal congruence θ on A. A connective f is called td-distributive if td)≈ f,…,td). If L is a propositional logic and V is a corresponding variety that has a TD term td, then any admissible in L rule, the premises of which contain only td-distributive operations, is derivable, and the (...)
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  5.  14
    A Meta-Logic of Inference Rules: Syntax.Alex Citkin - forthcoming - Logic and Logical Philosophy.
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  6.  22
    Metalogic of Intuitionistic Propositional Calculus.Alex Citkin - 2010 - Notre Dame Journal of Formal Logic 51 (4):485-502.
    With each superintuitionistic propositional logic L with a disjunction property we associate a set of modal logics the assertoric fragment of which is L . Each formula of these modal logics is interdeducible with a formula representing a set of rules admissible in L . The smallest of these logics contains only formulas representing derivable in L rules while the greatest one contains formulas corresponding to all admissible in L rules. The algebraic semantic for these logics is described.
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  7.  7
    Characteristic Formulas of Partial Heyting Algebras.Alex Citkin - 2013 - Logica Universalis 7 (2):167-193.
    The goal of this paper is to generalize a notion of characteristic (or Jankov) formula by using finite partial Heyting algebras instead of the finite subdirectly irreducible algebras: with every finite partial Heyting algebra we associate a characteristic formula, and we study the properties of these formulas. We prove that any intermediate logic can be axiomatized by such formulas. We further discuss the correlations between characteristic formulas of finite partial algebras and canonical formulas. Then with every well-connected Heyting algebra we (...)
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  8.  7
    Not Every Splitting Heyting or Interior Algebra is Finitely Presentable.Alex Citkin - 2012 - Studia Logica 100 (1-2):115-135.
    We give an example of a variety of Heyting algebras and of a splitting algebra in this variety that is not finitely presentable. Moreover, we show that the corresponding splitting pair cannot be defined by any finitely presentable algebra. Also, using the Gödel-McKinsey-Tarski translation and the Blok-Esakia theorem, we construct a variety of Grzegorczyk algebras with similar properties.
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  9.  1
    A Mind of a Non-Countable Set of Ideas.Alexander Citkin - 2008 - Logic and Logical Philosophy 17 (1-2):23-39.
    The paper is dedicated to the 80th birthday of the outstanding Russian logician A.V. Kuznetsov. It is addressing a history of the ideas and research conducted by him in non-classical and intermediate logics.
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