Translations and similarity-based logic programming

In order to provide approximate reasoning capabilities, in Gerla G, Sessa MI (1999) Chen G, Ying M, Cai K-Y (Eds) Fuzzy Logic and Soft computing, 19–31, Kluwer Academic Publishers, Boston an extension of Logic Programming has been proposed. Logic programs on function-free languages are considered, and approximate and imprecise information are represented by introducing a similarity relation ? in the set of predicate names and object names of the language. The inference system exploits the classical resolution rule of the Logic Programming paradigm. Moreover, the notion of fuzzy least Herbrand model is also provided. In this paper, by introducing the general notion of structural translation of languages, we generalize these results to the case of logic programs with function symbols. Some properties of the similarity relations are also proven.