Studia Logica

, Volume 50, Issue 1, pp 149–160 | Cite as

Predicate provability logic with non-modalized quantifiers

  • Giorgie Dzhaparidze


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 Q′GL, the Q′-fragment of the predicate version of the logic GL, we prove the recursive enumerability of the sets of Q′-formulas all arithmetical examples of which are: 1) T-provable, 2) true. In. particular, the first one is shown to be exactly Q′GL and the second one to be exactly the Q′-fragment of the predicate version of Solovay's logic S.


Mathematical Logic Computational Linguistic Modal Formula Arithmetical Formula Provability Logic 
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Copyright information

© Polish Academy of Sciences 1991

Authors and Affiliations

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

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