This paper gives a propositional reformulation of the fixed-point problem posed by Gupta and Belnap, using the stipulation logic of Visser. After presenting a solution for clones of three-valued operators that include the constant functions, I determine the maximal three-valued clones with constants that have the fixed-point property, giving different characterizations of them.
"Maximal Three-Valued Clones with the Gupta-Belnap Fixed-Point Property." Notre Dame J. Formal Logic 48 (4) 449 - 472, 2007. https://doi.org/10.1305/ndjfl/1193667704