This straightforwardly implies that propositional reasoning about provability in Peano Arithmetic is complete and decidable. Non-arithmeticity of truth predicate logics of provability. A simplified semantics, discovered by Tim Carlson, is often used for polymodal provability logics. In he did the same for the predicate provability logic with non-modalized quantifiers. In 1944, Alonzo Church emphasized that Gentzen's sequent assertions did not signify provability. However, these predicates have different properties from the point of view of provability in "T". Japaridze has also studied the first-order (predicate) versions of provability logic. Interpretability logics and Japaridze's polymodal logic present natural extensions of provability logic. He has also given it the subtitle "or The provability of any and every contention". Provability of consistency can then simply be added as an axiom.