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The issue of value invention in logic programming embraces many scenarios, such as logic programming with function symbols, object oriented logic languages, inter-operability with external sources of knowledge, or set unification. This work introduces a framework embedding value invention in a general context. The class of programs having a suitable (but, in general, not decidable) `finite grounding property' is identified, and the class of `value invention restricted' programs is introduced. Value invention restricted programs have the finite grounding property and can be decided in polynomial time. They are a very large polynomially decidable class having this property, when no assumption can be made about the nature of invented values (while this latter is the case in the specific literature about logic programming with function symbols). Relationships with existing formalisms are eventually discussed, and the implementation of a system supporting the class of such programs is described.