A connection between Similarity Logic Programming and Gödel Modal Logic

In this paper we relate two logical similarity-based approaches to approximate reasoning. One approach extends the framework of (propositional) classical logic programming by introducing a similarity relation in the alphabet of the language that allows for an extended unification procedure. The second approach is a many-valued modal logic approach where 3p is understood as approximately p. Here, the similarity relations are introduced at the level of the Kripke models where possible worlds can be similar to some extent. We show that the former approach can be expressed inside the latter.