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

We study a propositional polymodal provability logic GLP introduced by G. Japaridze. Previous treatments of this logic, due to Japaridze and Ignatiev, heavily relied on some non-finitary principles such as transfinite induction up to ε₀ or reflection ...

We introduce our implementation in HOL Light of the metatheory for Gödel–Löb provability logic (GL), covering soundness and completeness w.r.t. possible world semantics and featuring a prototype of a theorem prover for GL itself. The strategy we ...$\mathsf{}\mathsf{}\mathsf{}$

We introduce Kripke semantics for modal substructural logics, and prove the completeness theorems with respect to the semantics. The completeness theorems are proved using an extended Ishihara's method of canonical model construction (Ishihara, 2000). The ...