, Volume 4, Issue 2, pp 219-231

Automated proofs of Löb's theorem and Gödel's two incompletensess theorems

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Abstract

The modal logic calculus K4, which represents important properties of the provability relation of Peano's Arithmetic, is formalized within the automated reasoning system ITP. Very high level automated proofs are then obtained of Löb's theorem, and of Gödel's two incompleteness theorems.