Fuzzy unification and first order probabilistic logic

The notion of unification for fuzzy sets in fuzzy logic programming is explored in this article from the standpoint of a theoretical framework based on first-order probabilistic modal logic. The fundamental difference between the latter perspective and other approaches described in the literature lies in the characterization of fuzzy sets, which are construed in the logical framework as derived entities having a probabilistic deep structure. The analysis reveals that a few semantic unification techniques are sound even in this probabilistic approach, provided that some specific conditions are enforced. In addition, the approach helps to clarify some important aspects of the informal interpretation for the unification process, including a rationale for the applicability requisites of computational techniques. In the discussion, the reference model adopted for the notion of fuzzy unification is that of evidential logic programming, that is, the one underlying the programming language FRIL.