Modal logic Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability and/or various related metamathematical properties and relations such as weak interpretability, Π₁-conservativity, cointerpretability, tolerance, cotolerance, arithmetic complexities.

Main contributors to the field: Alessandro Berarducci, Petr Hájek, Konstantin Ignatiev, Giorgi Japaridze, Franco Montagna, Vladimir Shavrukov, Rineke Verbrugge, Albert Visser, Domenico Zambella.

References

• Giorgi Japaridze and Dick de Jongh, The Logic of Provability. In Handbook of Proof Theory, S.Buss, ed. Elsevier, 1998, pp. 475-546.