A Survey of Provability Logic

Provability logic is a kind of modal logic obtained by interpreting the alethic operator for necessity as an operator of provability. It is used mainly for proving results about selfreferential sentences in arithmetic. Very few writers have contributed to the topic of provability logic, especially considering its potential applications to deductive databases and distributed problem solving. This short survey is to a large extent based on publications by Boolos and Smorynski. 1This paper replaces Working Paper No.170, “A Survey of Provability Logic and a Note on its Relevance to Nonmonotonic Federated Information Systems”, published in June, 1990. Since then the author has given up on his ideas on using recursion theory for solving problems with nonmonotonic federated information systems. Because of the demand for WP170 over the last 18 months, it seems only fair to exclude those bits that do not seem relevant, and to concentrate on presenting a survey, now that WP170 is out of print. The author has taken this opportunity to revise the paper with respect to language and layout. He would also like to thank Paul Johannesson for comments on drafts of WP170, and also the people who have helped distribute that paper to the far corners of this world.