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Provability logic, or the logic of provability, is a modal logic where the "necessity" operator is interpreted as provability in a reasonably rich formal theory such as Peano arithmetic. It was pioneered by Robert Solovay in 1976. Since then until his passing in 1996 the prime inspirer of the field was
George Boolos. Significant contributions to the field have been made by
Sergei Artemov, Lev Beklemishev, Giorgi Japaridze, Dick de Jongh, Franco Montagna, Vladimir Shavrukov, Albert Visser and others.
Interpretability logics present natural extensions of
provability logic.
References
- George Boolos, The Logic of Provability. Cambridge University Press, 1993.
- Giorgi
Japaridze and Dick de Jongh, The logic
of Provability. In: Handbook of Proof Theory, S.Buss, ed. Elsevier, 1998, pp. 475-546.
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