11 found
  1.  28
    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 (...)
    Direct download (4 more)  
    Export citation  
    Bookmark   15 citations  
  2.  30
    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.
    Direct download  
    Export citation  
    Bookmark   11 citations  
  3.  39
    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.
    Direct download (8 more)  
    Export citation  
    Bookmark   10 citations  
  4.  46
    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. (...)
    Direct download (5 more)  
    Export citation  
    Bookmark   9 citations  
  5.  22
    Writing out unifiers for formulas with coefficients in intuitionistic logic.V. V. Rybakov - 2013 - Logic Journal of the IGPL 21 (2):187-198.
  6.  38
    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 (...)
    Direct download (4 more)  
    Export citation  
    Bookmark   5 citations  
  7.  35
    A modal analog for Glivenko's theorem and its applications.V. V. Rybakov - 1992 - Notre Dame Journal of Formal Logic 33 (2):244-248.
  8.  23
    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.
    Direct download (3 more)  
    Export citation  
    Bookmark   2 citations  
  9.  21
    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.
    Direct download  
    Export citation  
    Bookmark   1 citation  
  10.  22
    Handbook of the Logic of Argument and Inference.V. V. Rybakov - 2004 - Bulletin of Symbolic Logic 10 (2):220-222.
  11.  99
    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.
    Direct download (6 more)  
    Export citation