Uniqueness of fixpoints of single-step operators determined by Belnap's four-valued logic

Recently, Hitzler and Seda showed how a domain-theoretic proof can be given of the fact that, for a locally hierarchical program, the single-step operator TP , de�ned in two-valued logic, has a unique �xed point. Their approach employed a construction which turned a ScottErshov domain into a generalized ultrametric space. Finally, a �xed-point theorem of PriessCrampe and Ribenboim was applied to TP to establish the result. In this paper, we extend these methods and results to the corresponding well-known single-step operators �P and P determined by P and de�ned, respectively, in three-valued and four-valued logics