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Journal of Logic and Computation 2005 15(4):539-549; doi:10.1093/logcom/exi037
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Vol. 15 No. 4, © The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

On Kripke-style Semantics for the Provability Logic of Gödel's Proof Predicate with Quantifiers on Proofs

Rostislav Yavorskiy

V.A. Steklov Mathematical Institute, Gubkina 8, 119991 Moscow, Russia. Email: rey{at}mi.ras.ru

Kripke-style semantics is suggested for the provability logic with quantifiers on proofs corresponding to the standard Gödel proof predicate. It is proved that the set of valid formulas is decidable. The arithmetical completeness is still an open issue.

Keywords: Provability logic, logic of proofs, Kripke semantics, decidability

Received May 2005.


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