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Studia Logica

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

Predicate provability logic with non-modalized quantifiers

  • Giorgie Dzhaparidze
Article

Abstract

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.

Keywords

Mathematical Logic Computational Linguistic Modal Formula Arithmetical Formula Provability Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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