Remarks of the Gupta-Belnap Fixed-Point Property for k-valued Clones

The main objective of this paper is to prove that certain families of k-valued clones have the Gupta-Belnap fixed-point property. This, essentially, means that all propositional languages that are interpreted with operators belonging to those clones are such that any net of self-referential sentences can be consistently evaluated. The results will be applied to study some expansions of the four-valued clones due to Belnap and Fitting.