21 found
Order:
  1.  14
    The Logic of Generalized Truth Values and the Logic of Bilattices.Sergei P. Odintsov & Heinrich Wansing - 2015 - Studia Logica 103 (1):91-112.
    This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative and distributive (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  2.  43
    On Axiomatizing Shramko-Wansing’s Logic.Sergei P. Odintsov - 2009 - Studia Logica 91 (3):407 - 428.
    This work treats the problem of axiomatizing the truth and falsity consequence relations, $ \vDash _t $ and $ \vDash _f $, determined via truth and falsity orderings on the trilattice SIXTEEN₃. The approach is based on a representation of SIXTEEN₃ as a twist-structure over the two-element Boolean algebra.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  3.  13
    Disentangling FDE -Based Paraconsistent Modal Logics.Sergei P. Odintsov & Heinrich Wansing - 2017 - Studia Logica 105 (6):1221-1254.
    The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absurdity constant. Moreover, (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  4.  41
    On the Representation of N4-Lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.
    N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  5.  12
    On Axiomatizing Shramko-Wansing’s Logic.Sergei P. Odintsov - 2009 - Studia Logica 91 (3):407-428.
    This work treats the problem of axiomatizing the truth and falsity consequence relations, $ \vDash _t $ and $ \vDash _f $, determined via truth and falsity orderings on the trilattice SIXTEEN₃. The approach is based on a representation of SIXTEEN₃ as a twist-structure over the two-element Boolean algebra.
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   11 citations  
  6. On Algorithmic Properties of Propositional Inconsistency-Adaptive Logics.Sergei P. Odintsov & Stanislav O. Speranski - 2012 - Logic and Logical Philosophy 21 (3):209-228.
    The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  7
    Belnap–Dunn Modal Logics: Truth Constants Vs. Truth Values.Sergei P. Odintsov & Stanislav O. Speranski - forthcoming - Review of Symbolic Logic:1-20.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  6
    The Lattice of Belnapian Modal Logics: Special Extensions and Counterparts.Sergei P. Odintsov & Stanislav O. Speranski - 2016 - Logic and Logical Philosophy 25 (1):3-33.
    Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  9.  40
    The Class of Extensions of Nelson's Paraconsistent Logic.Sergei P. Odintsov - 2005 - Studia Logica 80 (2-3):291-320.
    The article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  10.  7
    Hintikka’s Independence-Friendly Logic Meets Nelson’s Realizability.Sergei P. Odintsov, Stanislav O. Speranski & Igor Yu Shevchenko - 2018 - Studia Logica 106 (3):637-670.
    Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics for independence-friendly first-order logic, but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  11.  12
    On Definability of Connectives and Modal Logics Over FDE.Sergei P. Odintsov, Daniel Skurt & Heinrich Wansing - forthcoming - Logic and Logical Philosophy:1.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  12.  23
    BK-Lattices. Algebraic Semantics for Belnapian Modal Logics.Sergei P. Odintsov & E. I. Latkin - 2012 - Studia Logica 100 (1-2):319-338.
    Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK -lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK -lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK . Finally, we describe invariants determining a twist-structure over a (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  13.  11
    Logic of Classical Refutability and Class of Extensions of Minimal Logic.Sergei P. Odintsov - 2001 - Logic and Logical Philosophy 9:91.
  14.  14
    On the Structure of Paraconsistent Extensions of Johansson's Logic.Sergei P. Odintsov - 2005 - Journal of Applied Logic 3 (1):43-65.
  15.  7
    Priestley Duality for Paraconsistent Nelson’s Logic.Sergei P. Odintsov - 2010 - Studia Logica 96 (1):65-93.
  16.  21
    Negative Equivalence of Extensions of Minimal Logic.Sergei P. Odintsov - 2004 - Studia Logica 78 (3):417-442.
    Two logics L1 and L2 are negatively equivalent if for any set of formulas X and any negated formula ¬, ¬ can be deduced from the set of hypotheses X in L1 if and only if it can be done in L2. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  30
    On Deductive Bases for Partial Equilibrium Logic.Sergei P. Odintsov - 2012 - Bulletin of the Section of Logic 41 (3/4):199-213.
    Direct download  
     
    Export citation  
     
    Bookmark  
  18.  17
    Computability Issues for Adaptive Logics in Multi-Consequence Standard Format.Sergei P. Odintsov & Stanislav O. Speranski - 2013 - Studia Logica 101 (6):1237-1262.
    In a rather general setting, we prove a number of basic theorems concerning computational complexity of derivability in adaptive logics. For that setting, the so-called standard format of adaptive logics is suitably adopted, and the corresponding completeness results are established in a very uniform way.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  19. Absurdity as Unary Operator.Sergei P. Odintsov - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):225-242.
    It was shown in the previous work of the author that one can avoid the paradox of minimal logic { ϕ , ¬ ϕ } ¬ ψ defining the negation operator via reduction not a constant of absurdity, but to a unary operator of absurdity. In the present article we study in details what does it mean that negation in a logical system can be represented via an absurdity or contradiction operator. We distinguish different sorts of such presentations. Finally, we (...)
     
    Export citation  
     
    Bookmark  
  20.  9
    From the Guest Editors.Alexei Y. Muravitsky & Sergei P. Odintsov - 2008 - Logic and Logical Philosophy 17 (1-2):5-7.
    On the 28th of October, 2006, Alexander Vladimirovich Kuznetsov, so is his full name, would have turned 80. Although belated, the editorial board of Logic and Logical Philosophy, we, the editors and contributors of the present issue, and other members of the logic community mark this event with the present issue. Most of those who contributed to it knew Kuznetsov in person and/or were influenced by him or by his ideas, which very often resided in somebody else’s papers or became (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  21.  11
    Priestley Duality for Paraconsistent Nelson’s Logic.Sergei P. Odintsov - 2010 - Studia Logica 96 (1):65-93.
    The variety of N4? -lattices provides an algebraic semantics for the logic N4?, a version of Nelson 's logic combining paraconsistent strong negation and explosive intuitionistic negation. In this paper we construct the Priestley duality for the category of N4?-lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations