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The introduction of negation into logic programming brings the benefit of enhanced syntax and expressibility, but creates some semantical problems. Specifically, certain operators which are monotonic in the absence of negation become non-monotonic when it is introduced, with the result that standard approaches to denotational semantics then become inapplicable. In this paper, we show how generalized metric spaces can be used to obtain fixed-point semantics for several classes of programs relative to the supported model semantics, and investigate relationships between the underlying spaces we employ. Our methods allow the analysis of classes of programs which include the acyclic, locally hierarchical, and acceptable programs, amongst others, and draw on fixed-point theorems which apply to generalized ultrametric spaces and to partial metric spaces.