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Logic programming and ultrametric spaces

By this expository paper we would like to call the attention to ultrametric spaces and their applications to logic programming. We present the essentials of logic programming and give an introduction to the theory of ultrametric spaces. For these, we prove a fixed point theorem and also a multivalued fixed point theorem. The fixed point theorem is used to derive a criterion for the existence of a Herbrand model for a program which is not assumed to be positive.