## Works by Alex Citkin

14 found
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 Alex Citkin [14] Alexander Citkin [2]
1. Hereditarily structurally complete positive logics.Alex Citkin - 2020 - Review of Symbolic Logic 13 (3):483-502.
Positive logics are $\{ \wedge, \vee, \to \}$-fragments of intermediate logics. It is clear that the positive fragment of $Int$ is not structurally complete. We give a description of all hereditarily structurally complete positive logics, while the question whether there is a structurally complete positive logic which is not hereditarily structurally complete, remains open.

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2. Unified Deductive Systems: An Outline.Alex Citkin - 2023 - Logica Universalis 17 (4):483-509.
Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and obeying treated in the same way. The suggested approach is based on the ideas of Łukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. More precisely, a consequence relation is defined on a set of statements of forms “proposition _A_ is accepted” and “proposition _A_ is rejected”, where _A_ is (...)

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3. A meta-logic of inference rules: Syntax.Alex Citkin - 2015 - Logic and Logical Philosophy 24 (3).

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4. A note on admissible rules and the disjunction property in intermediate logics.Alexander Citkin - 2012 - Archive for Mathematical Logic 51 (1):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 that (...)

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5. Hereditarily Structurally Complete Superintuitionistic Deductive Systems.Alex Citkin - 2018 - Studia Logica 106 (4):827-856.
Propositional logic is understood as a set of theorems defined by a deductive system: a set of axioms and a set of rules. Superintuitionistic logic is a logic extending intuitionistic propositional logic \. A rule is admissible for a logic if any substitution that makes each premise a theorem, makes the conclusion a theorem too. A deductive system \ is structurally complete if any rule admissible for the logic defined by \ is derivable in \. It is known that any (...)

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6. Preface to the Rejection Special Issue.Alex Citkin & Alexei Muravitsky - 2023 - Logica Universalis 17 (4):405-410.

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7. 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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8. 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. V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics.Alex Citkin & Ioannis M. Vandoulakis (eds.) - 2022 - Springer, Outstanding Contributions To Logic (volume 24).
This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory (...)

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10. 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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11. 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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12. 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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13. 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 (...)