Interpretability logic
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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, Peter Hajek, Konstantin Ignatiev, Giorgi Japaridze, Franco Montagna, Vladimir Shavrukov, Rineke Verbrugge, Albert Visser, Domenico Zambella.
References
- Giorgi Japaridze (http://www.csc.villanova.edu/~japaridz/) and Dick de Jongh, The Logic of Provability. In Handbook of Proof Theory, S.Buss, ed. Elsevier, 1998, pp. 475-546.