# Category: Provability logic

Interpretability logic
Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability or various related metamathematical properties and relations such as weak interpret
Löb's theorem
In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true",
Hilbert–Bernays provability conditions
In mathematical logic, the Hilbert–Bernays provability conditions, named after David Hilbert and Paul Bernays, are a set of requirements for formalized provability predicates in formal theories of ari
Japaridze's polymodal logic
Japaridze's polymodal logic (GLP) is a system of provability logic with infinitely many provability modalities. This system has played an important role in some applications of provability algebras in
Provability logic
Provability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich for