Complex sentence: Provability logic is a modal logic where the box (or "necessity") operator is interpreted as'it is provable that', capturing the notion of a proof predicate of a reasonably rich formal theory such as Peano arithmetic.
Split into simpler sentences: 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 formal theory, such as Peano arithmetic.