6 found
Order:
  1.  22
    Sergei Artemov & Giorgie Dzhaparidze (1990). Finite Kripke Models and Predicate Logics of Provability. Journal of Symbolic Logic 55 (3):1090-1098.
    The paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic: If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that $PA \nvdash fR$ . This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of QGL and QS). The proof was obtained by adding "the predicate part" as a specific (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  2.  11
    Giorgie Dzhaparidze (1992). The Logic of Linear Tolerance. Studia Logica 51 (2):249 - 277.
    A nonempty sequence T1,...,Tn of theories is tolerant, if there are consistent theories T 1 + ,..., T n + such that for each 1 i n, T i + is an extension of Ti in the same language and, if i n, T i + interprets T i+1 + . We consider a propositional language with the modality , the arity of which is not fixed, and axiomatically define in this language the decidable logics TOL and TOL. It is (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  3.  4
    Giorgie Dzhaparidze (1993). A Generalized Notion of Weak Interpretability and the Corresponding Modal Logic. Annals of Pure and Applied Logic 61 (1-2):113-160.
    Dzhaparidze, G., A generalized notion of weak interpretability and the corresponding modal logic, Annals of Pure and Applied Logic 61 113-160. A tree Tr of theories T1,...,Tn is called tolerant, if there are consistent extensions T+1,...,T+n of T1,...,Tn, where each T+i interprets its successors in the tree Tr. We consider a propositional language with the following modal formation rule: if Tr is a tree of formulas, then Tr is a formula, and axiomatically define in this language the decidable logics TLR (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  4.  9
    Giorgie Dzhaparidze (1990). Decidable and Enumerable Predicate Logics of Provability. Studia Logica 49 (1):7 - 21.
    Predicate modal formulas are considered as schemata of arithmetical formulas, where is interpreted as the standard formula of provability in a fixed sufficiently rich theory T in the language of arithmetic. QL T(T) and QL T are the sets of schemata of T-provable and true formulas, correspondingly. Solovay's well-known result — construction an arithmetical counterinterpretation by Kripke countermodel — is generalized on the predicate modal language; axiomatizations of the restrictions of QL T(T) and QL T by formulas, which contain no (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  5.  18
    Giorgie Dzhaparidze (1991). Predicate Provability Logic with Non-Modalized Quantifiers. Studia Logica 50 (1):149 - 160.
    Predicate modal formulas with non-modalized quantifiers (call them Q-formulas) are considered as schemata of arithmetical formulas, where is interpreted as the provability predicate of some fixed correct extension T of arithmetic. A method of constructing 1) non-provable in T and 2) false arithmetical examples for Q-formulas by Kripke-like countermodels of certain type is given. Assuming the means of T to be strong enough to solve the (undecidable) problem of derivability in QGL, the Q-fragment of the predicate version of the logic (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  6.  3
    Giorgie Dzhaparidze (1994). The Logic of Arithmetical Hierarchy. Annals of Pure and Applied Logic 66 (2):89-112.
    Formulas of the propositional modal language with the unary modal operators □, Σ1, 1, Σ2, 2,… are considered as schemata of sentences of arithmetic , where □A is interpreted as “A is PA-provable”, ΣnA as “A is PA-equivalent to a Σn-sentence” and nA as “A is PA-equivalent to a Boolean combination of Σn-sentences”. We give an axiomatization and show decidability of the sets of the modal formulas which are schemata of: PA-provable, true arithmetical sentences.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography