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Interpolation Properties for the Bimodal Provability Logic GR

English (英語)

Studia Logica

Springer Nature

2025-02-05

2025-03-04

Published online: 05 February 2025

We study interpolation properties for Shavrukov’s bimodal logic GR of usual and Rosser provability predicates. For this purpose, we introduce a new sublogic GR◦ of GR and its relational semantics. Based on our new semantics, we prove that GR◦ and GR enjoy Lyndon interpolation property and uniform interpolation property. As a consequence of our proofs, we obtain the completeness and the finite frame property of GR◦ and GR and with respect to our new semantics.

Interpolation properties

学術雑誌論文

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