D. Leviant; 1981; "On the proof theory of the modal logic for arithmetic provability"
Memo
R. Goré, R. Ramanayake; 2008; "Valentini's Cut-Elimination for Provability Logic Resolved"
によると，
S. Valentini; 1983; "The Modal Logic of Provability: Cut-Elimination"
にで証明にミスがあることが指摘されている．