6 found
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  1.  74
    Finite Kripke models and predicate logics of provability.Sergei Artemov & Giorgie Dzhaparidze - 1990 - 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 (...)
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  2.  17
    A generalized notion of weak interpretability and the corresponding modal logic.Giorgie Dzhaparidze - 1993 - 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 (...)
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  3.  20
    The logic of arithmetical hierarchy.Giorgie Dzhaparidze - 1994 - 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.
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  4.  42
    The logic of linear tolerance.Giorgie Dzhaparidze - 1992 - 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 (...)
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  5.  35
    Decidable and enumerable predicate logics of provability.Giorgie Dzhaparidze - 1990 - 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 (...)
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  6.  43
    Predicate provability logic with non-modalized quantifiers.Giorgie Dzhaparidze - 1991 - 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 (...)
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