Sibylla Priess-Crampe and Paulo Ribenboim recently established a general fixed-point theorem for multivalued mappings defined on generalized ultrametric spaces, and introduced it to the area of logic programming semantics. We discuss, in this context, the applications which have been made so far of this theorem and of its corollaries. In particular, we will relate these results to Scott-Ershov domains, familiar in programming language semantics, and to the generalized metrics of Khamsi, Kreinovich, and Misane which have been applied, by these latter authors, to logic programming. Amongst other things, we will also show that a unified treatment of the fixed-point theory of wide classes of programs can be given by means of the theorems of Priess-Crampe and Ribenboim.
& Seda, A. K.
(2002). The Fixed-Point Theorems of Priess-Crampe and Ribenboim in Logic Programming. Valuation Theory and its Applications, 1, 219-235.