Interpretability logic is a family of modal logics that extend provability logic to describe various metamathematical properties and relations such as provability, interpretability, conservativity, cointerpretability, tolerance, cotolerance, arithemtic complexities.

Historical notes

Being inspired by the success achieved in provability logic, the study of interpretability logics began at the late 1980s Main contributors to the field: Alessandro Berarducci, Konstantin Ignatiev, Giorgi Japaridze, Vladimir Shavrukov, Rineke Verbrugge, Albert Visser, Domenico Zambella.

References

Giorgi Japaridze and Dick de Yongh, The Logic of Provability. In Handbook of Proof Theory, S.Buss, ed., Elsevier, 1998.