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  1. V. V. Rimatski & V. V. Rybakov (2005). A Note on Globally Admissible Inference Rules for Modal and Superintuitionistic Logics. Bulletin of the Section of Logic 34 (2):93-99.
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  2. V. V. Rybakov (2005). Logical Consecutions in Discrete Linear Temporal Logic. 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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  3. V. V. Rybakov (2004). Handbook of the Logic of Argument and Inference. Bulletin of Symbolic Logic 10 (2):220-222.
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  4. V. V. Rybakov (2003). Barwise's Information Frames and Modal Logics. 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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  5. V. V. Rybakov (2003). Refined Common Knowledge Logics or Logics of Common Information. 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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  6. V. V. Rybakov (2001). Construction of an Explicit Basis for Rules Admissible in Modal System S4. Mathematical Logic Quarterly 47 (4):441-446.
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  7. V. V. Rybakov, M. Terziler & C. Gencer (2000). On Self-Admissible Quasi-Characterizing Inference Rules. 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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  8. V. V. Rybakov, M. Terziler & C. Gencer (2000). Unification and Passive Inference Rules for Modal Logics. 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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  9. V. V. Rybakov, M. Terziler & V. Remazki (2000). A Basis in Semi-Reduced Form for the Admissible Rules of the Intuitionistic Logic IPC. Mathematical Logic Quarterly 46 (2):207-218.
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  10. V. V. Rybakov, M. Terziler & C. Gencer (1999). An Essay on Unification and Inference Rules for Modal Logics. Bulletin of the Section of Logic 28 (3):145-157.
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  11. V. V. Rybakov (1995). Hereditarily Structurally Complete Modal Logics. 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. V. V. Rybakov (1992). A Modal Analog for Glivenko's Theorem and its Applications. Notre Dame Journal of Formal Logic 33 (2):244-248.
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  13. V. V. Rybakov (1990). Logical Equations and Admissible Rules of Inference with Parameters in Modal Provability Logics. 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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  14. V. V. Rybakov (1990). Problems of Substitution and Admissibility in the Modal System Grz and in Intuitionistic Propositional Calculus. Annals of Pure and Applied Logic 50 (1):71-106.
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