Provability logic, or the logic of provability, is a modal logic where the modal "necessity" operator is interpreted as provability in a reasonably rich formal theory such as Peano arithmetic.

Historical survey

Pioneered by Robert Solovay in 1976. Since then until his passing 1n 1997 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.

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.