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Vladimir V. Rybakov [14]V. V. Rybakov [11]V. Rybakov [9]Vladimir Rybakov [7]
Vladimir Vladimir Rybakov [1]
  1.  50
    Admissibility of Logical Inference Rules.Vladimir Vladimir Rybakov - 1997 - Elsevier.
    The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special (...)
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  2. Rules of Inference with Parameters for Intuitionistic Logic.Vladimir V. Rybakov - 1992 - Journal of Symbolic Logic 57 (3):912-923.
    An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability of logical equations (...)
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  3.  32
    Unification in Linear Temporal Logic LTL.Sergey Babenyshev & Vladimir Rybakov - 2011 - Annals of Pure and Applied Logic 162 (12):991-1000.
    We prove that a propositional Linear Temporal Logic with Until and Next has unitary unification. Moreover, for every unifiable in LTL formula A there is a most general projective unifier, corresponding to some projective formula B, such that A is derivable from B in LTL. On the other hand, it can be shown that not every open and unifiable in LTL formula is projective. We also present an algorithm for constructing a most general unifier.
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  4.  15
    Unification and Admissible Rules for Paraconsistent Minimal Johanssonsʼ Logic J and Positive Intuitionistic Logic IPC.Sergei Odintsov & Vladimir Rybakov - 2013 - Annals of Pure and Applied Logic 164 (7-8):771-784.
    We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just unifiability (...)
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  5.  13
    Problems of Substitution and Admissibility in the Modal System Grz and in Intuitionistic Propositional Calculus.V. V. Rybakov - 1990 - Annals of Pure and Applied Logic 50 (1):71-106.
    Questions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework. The main result is the decidability of the universal theory of the free modal algebra imageω extended in signature by adding constants for free generators. As corollaries we obtain: there exists an algorithm for the recognition of admissibility of rules with parameters in the modal system Grz, the substitution problem for Grz and for (...)
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  6.  25
    Construction of an Explicit Basis for Rules Admissible in Modal System S4.Vladimir V. Rybakov - 2001 - Mathematical Logic Quarterly 47 (4):441-446.
    We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra ℱS4 of countable rank.
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  7.  13
    Linear Temporal Logic with Until and Next, Logical Consecutions.V. Rybakov - 2008 - Annals of Pure and Applied Logic 155 (1):32-45.
    While specifications and verifications of concurrent systems employ Linear Temporal Logic , it is increasingly likely that logical consequence in image will be used in the description of computations and parallel reasoning. Our paper considers logical consequence in the standard image with temporal operations image and image . The prime result is an algorithm recognizing consecutions admissible in image, so we prove that image is decidable w.r.t. admissible inference rules. As a consequence we obtain algorithms verifying the validity of consecutions (...)
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  8.  18
    Writing Out Unifiers for Formulas with Coefficients in Intuitionistic Logic.V. V. Rybakov - 2013 - Logic Journal of the IGPL 21 (2):187-198.
  9.  19
    An Essay on Unification and Inference Rules for Modal Logics.V. V. Rybakov, M. Terziler & C. Gencer - 1999 - Bulletin of the Section of Logic 28 (3):145-157.
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  10.  33
    Logical Consecutions in Discrete Linear Temporal Logic.V. V. Rybakov - 2005 - Journal of Symbolic Logic 70 (4):1137 - 1149.
    We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. (...)
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  11.  29
    Hereditarily Structurally Complete Modal Logics.V. V. Rybakov - 1995 - Journal of Symbolic Logic 60 (1):266-288.
    We consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete $\operatorname{iff} \lambda$ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular.
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  12.  24
    On Finite Model Property for Admissible Rules.Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner - 1999 - Mathematical Logic Quarterly 45 (4):505-520.
    Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...)
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  13. Axiomatizing the Next-Interior Fragment of Dynamic Topological Logic.Philip Kremer, Grigori Mints & V. Rybakov - 1997 - Bulletin of Symbolic Logic 3:376-377.
  14.  8
    Unifiers in Transitive Modal Logics for Formulas with Coefficients.V. Rybakov - 2013 - Logic Journal of the IGPL 21 (2):205-215.
  15.  33
    Logical Equations and Admissible Rules of Inference with Parameters in Modal Provability Logics.V. V. Rybakov - 1990 - Studia Logica 49 (2):215 - 239.
    This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman''s problem forGL andS. We also show that A. V. Kuznetsov''s problem of the existence of finite basis for admissible rules forGL andS has a negative solution. Afterwards we (...)
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  16.  26
    Criteria for Admissibility of Inference Rules. Modal and Intermediate Logics with the Branching Property.Vladimir V. Rybakov - 1994 - Studia Logica 53 (2):203 - 225.
    The main result of this paper is the following theorem: each modal logic extendingK4 having the branching property belowm and the effective m-drop point property is decidable with respect to admissibility. A similar result is obtained for intermediate intuitionistic logics with the branching property belowm and the strong effective m-drop point property. Thus, general algorithmic criteria which allow to recognize the admissibility of inference rules for modal and intermediate logics of the above kind are found. These criteria are applicable to (...)
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  17.  26
    A Modal Analog for Glivenko's Theorem and its Applications.V. V. Rybakov - 1992 - Notre Dame Journal of Formal Logic 33 (2):244-248.
  18.  27
    Best Unifiers in Transitive Modal Logics.Vladimir V. Rybakov - 2011 - Studia Logica 99 (1-3):321-336.
    This paper offers a brief analysis of the unification problem in modal transitive logics related to the logic S4 : S4 itself, K4, Grz and Gödel-Löb provability logic GL . As a result, new, but not the first, algorithms for the construction of ‘best’ unifiers in these logics are being proposed. The proposed algorithms are based on our earlier approach to solve in an algorithmic way the admissibility problem of inference rules for S4 and Grz . The first algorithms for (...)
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  19.  18
    Even Tabular Modal Logics Sometimes Do Not Have Independent Base for Admissible Rules.Vladimir V. Rybakov - 1995 - Bulletin of the Section of Logic 24 (1):37-40.
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  20.  80
    On Self-Admissible Quasi-Characterizing Inference Rules.V. V. Rybakov, M. Terziler & C. Gencer - 2000 - Studia Logica 65 (3):417-428.
    We study quasi-characterizing inference rules (this notion was introduced into consideration by A. Citkin (1977). The main result of our paper is a complete description of all self-admissible quasi-characterizing inference rules. It is shown that a quasi-characterizing rule is self-admissible iff the frame of the algebra generating this rule is not rigid. We also prove that self-admissible rules are always admissible in canonical, in a sense, logics S4 or IPC regarding the type of algebra generating rules.
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  21.  13
    A Basis in Semi-Reduced Form for the Admissible Rules of the Intuitionistic Logic IPC.Vladimir V. Rybakov, Mehmet Terziler & Vitaliy Remazki - 2000 - Mathematical Logic Quarterly 46 (2):207-218.
    We study the problem of finding a basis for all rules admissible in the intuitionistic propositional logic IPC. The main result is Theorem 3.1 which gives a basis consisting of all rules in semi-reduced form satisfying certain specific additional requirements. Using developed technique we also find a basis for rules admissible in the logic of excluded middle law KC.
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  22. Temporal Logic with Interacting Agents.Vladimir V. Rybakov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):293-308.
  23.  6
    Intermediate Logics Preserving Admissible Inference Rules of Heyting Calculus.Vladimir V. Rybakov - 1993 - Mathematical Logic Quarterly 39 (1):403-415.
    The aim of this paper is to look from the point of view of admissibility of inference rules at intermediate logics having the finite model property which extend Heyting's intuitionistic propositional logic H. A semantic description for logics with the finite model property preserving all admissible inference rules for H is given. It is shown that there are continuously many logics of this kind. Three special tabular intermediate logics λ, 1 ≥ i ≥ 3, are given which describe all tabular (...)
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  24.  27
    Barwise's Information Frames and Modal Logics.Vladimir V. Rybakov - 2003 - Archive for Mathematical Logic 42 (3):261-277.
    The paper studies Barwise's information frames and answers the John Barwise question: to find axiomatizations for the modal logics generated by information frames. We find axiomatic systems for (i) the modal logic of all complete information frames, (ii) the logic of all sound and complete information frames, (iii) the logic of all hereditary and complete information frames, (iv) the logic of all complete, sound and hereditary information frames, and (v) the logic of all consistent and complete information frames. The notion (...)
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  25.  4
    Description of Modal Logics Inheriting Admissible Rules for S4.V. Rybakov - 1999 - Logic Journal of the IGPL 7 (5):655-664.
    We give a necessary and sufficient condition for any modal logic with fmp to inherit all inference rules admissible in S4. Using this condition we describe all tabular modal logics inheriting inference rules admissible for S4.
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  26.  20
    A Necessary Condition for Rules to Be Admissible in Temporal Tomorrow-Logic.M. I. Golovanov, Vladimir V. Rybakov & E. M. Yurasova - 2003 - Bulletin of the Section of Logic 32 (4):213-220.
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  27.  17
    Decidability: Theorems and Admissible Rules.Vladimir Rybakov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):293-308.
    The paper deals with a temporal multi-agent logic TMAZ, which imitates taking of decisions based on agents' access to knowledge by their interaction. The interaction is modelled by possible communication channels between agents in special temporal Kripke/hintikka-like models. The logic TMAZ distinguishes local and global decisions-making. TMAZ is based on temporal Kripke/hintikka models with agents' accessibility relations defined on states of all possible time clusters C. The main result provides a decision algorithm for TMAZ. This algorithm also solves the satisfiability (...)
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  28.  15
    Projective Formulas and Unification in Linear Temporal Logic LTLU.V. Rybakov - 2014 - Logic Journal of the IGPL 22 (4):665-672.
  29.  17
    Handbook of the Logic of Argument and Inference.V. V. Rybakov - 2004 - Bulletin of Symbolic Logic 10 (2):220-222.
  30.  16
    An Axiomatisation for the Multi-Modal Logic of Knowledge and Linear Time LTK.Erica Calardo & Vladimir Rybakov - 2007 - Logic Journal of the IGPL 15 (3):239-254.
    The paper aims at providing the multi-modal propositional logic LTK with a sound and complete axiomatisation. This logic combines temporal and epistemic operators and focuses on m odeling the behaviour of a set of agents operating in a system on the background of a temporal framework. Time is represented as linear and discrete, whereas knowledge is modeled as an S5-like modality. A further modal operator intended to represent environment knowledge is added to the system in order to achieve the expressive (...)
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  31.  13
    Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility.Sergei Odintsov & Vladimir Rybakov - 2015 - Logica Universalis 9 (1):93-120.
    Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – (...)
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  32.  11
    Logics of Schemes for First-Order Theories and Poly-Modal Propositional Logic.Vladimir V. Rybakov - 1997 - In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer Academic Publishers. pp. 93--106.
  33.  19
    A Note on Globally Admissible Inference Rules for Modal and Superintuitionistic Logics.V. V. Rimatski & V. V. Rybakov - 2005 - Bulletin of the Section of Logic 34 (2):93-99.
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  34.  10
    Combining Time and Knowledge, Semantic Approach.Erica Calardo & Vladimir V. Rybakov - 2005 - Bulletin of the Section of Logic 34 (1):13-21.
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  35.  23
    Refined Common Knowledge Logics or Logics of Common Information.Vladimir V. Rybakov - 2003 - Archive for Mathematical Logic 42 (2):179-200.
    In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe their connections and give dividing examples. Also (...)
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  36.  9
    Discrete Linear Temporal Logic with Current Time Point Clusters, Deciding Algorithms.V. Rybakov - 2008 - Logic and Logical Philosophy 17 (1-2):143-161.
    The paper studies the logic TL(NBox+-wC) – logic of discrete linear time with current time point clusters. Its language uses modalities Diamond+ (possible in future) and Diamond- (possible in past) and special temporal operations, – Box+w (weakly necessary in future) and Box-w (weakly necessary in past). We proceed by developing an algorithm recognizing theorems of TL(NBox+-wC), so we prove that TL(NBox+-wC) is decidable. The algorithm is based on reduction of formulas to inference rules and converting the rules in special reduced (...)
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  37.  13
    Unification and Passive Inference Rules for Modal Logics.V. V. Rybakov, M. Terziler & C. Gencer - 2000 - Journal of Applied Non-Classical Logics 10 (3-4):369-377.
    ABSTRACT We1 study unification of formulas in modal logics and consider logics which are equivalent w.r.t. unification of formulas. A criteria is given for equivalence w.r.t. unification via existence or persistent formulas. A complete syntactic description of all formulas which are non-unifiable in wide classes of modal logics is given. Passive inference rules are considered, it is shown that in any modal logic over D4 there is a finite basis for passive rules.
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