Studia Logica

, Volume 49, Issue 1, pp 7–21 | Cite as

Decidable and enumerable predicate logics of provability

  • Giorgie Dzhaparidze


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. QLT(T) and QLT 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 QLT(T) and QLT by formulas, which contain no variables different from x, are given by means of decidable prepositional bimodal systems; under the assumption that T is Π1-complete, there is established the enumerability of the restrictions of QLT(T) and QLT by: 1) formulas in which the domains of different occurrences of □ don't intersect and 2) formulas of the form n ⊥ → A.


Mathematical Logic Computational Linguistic Standard Formula Predicate Logic Modal Language 
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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Giorgie Dzhaparidze
    • 1
  1. 1.Academy of Sciences of Georgian SSRInstitute of PhilosophyTbilisiUSSR

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