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We define here a formal notion of finite representation of infinite query answers in logic programs. We apply this notion to DatalognS programs may be infinite and consequently queries may have infinite answers.We present a method to finitely represent infinite least Herbrand models of DatalognS program (and its underlying computational engine) can be forgotten. Given a query to be evaluated, it is easy to obtain from the relational specification finitely many answer substitutions that represent infinitely many answer substitutions to the query. The method involved is a combination of a simple, unificationless, computational mechanism (graph traversal, congruence closure, or term rewriting) and standard relational query evaluation methods. Second, a relational specification is effectively computable and its computation is no harder, in the sense of the complexity class, than answering yes-no queries.Our method is applicable to every range-restricted DatalognS program. We also show that for some very simple non-DatalognS logic programs, finite representations of query answers do not exist.