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Vladimir V. Rybakov [14]Vladimir Vladimir Rybakov [1]
  1.  66
    Admissibility of logical inference rules.Vladimir Vladimir Rybakov - 1997 - New York: 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.  28
    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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  4.  28
    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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  5.  28
    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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  6.  35
    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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  7.  23
    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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  8.  24
    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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  9.  10
    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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  10.  15
    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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  11.  24
    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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  12.  31
    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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  13.  13
    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.
  14.  31
    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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  15. Temporal logic with interacting agents.Vladimir V. Rybakov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):293-308.
     
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