On Two Models of Provability

Generalized Veltman models with a root

Provability logic is a nonstandard modal logic. Interpretability logic is an extension of provability logic. Generalized Veltman models are Kripke like semantics for interpretability logic. We consider generalized Veltman models with a root, i.e. r-validity, r-satisfiability and a consequence relation. We modify Fine’s and Rautenberg’s proof and prove non–compactness of interpretability logic.

Models of the Polymodal Provability Logic

Bisimulation quotients of Veltman models

Interpretability logic is a modal description of the interpretability predicate. The modal system IL is an extension of the provability logic GL (Gödel–Löb). Bisimulation quotients and largest bisimulations have been well studied for Kripke models. We examine interpretability logic and consider how these results extend to Veltman models. REPORTS ON MATHEMATICAL LOGIC 40 (2006), 59–73 Domagoj VR...

Constructive Provability Logic 1

We present two variants of an intuitionistic sequent calculus that validates the Löb rule and permits logical reflection over provability. We explore properties of both variants of this logic, which we call constructive provability logic due to its close ties to Gödel-Löb provability logic.

On topological models of GLP

We develop topological semantics of a polymodal provability logic GLP. Our main result states that the bimodal fragment of GLP, although incomplete with respect to relational semantics, is topologically complete. The topological (in)completeness of GLP remains an interesting open problem.