An efficient fuzzy unification method and its implementation into the Bousi~Prolog system

Bousi~Prolog is a fuzzy logic programming language whose main objective is to make flexible the query answering process. Its operational mechanism is a extension of the SLD-resolution (called weak resolution) where the classical syntactic unification algorithm has been replaced by a fuzzy one. This paper presents a generic method for the unification of linguistic terms (i.e. fuzzy sets) which is also applicable to other programming languages with an operational semantics based on some kind of weak resolution mechanism. The basic idea is to compile the information provided by fuzzy sets, generating a binary fuzzy relation on the set of their associated linguistic labels. Subsequently, this fuzzy relation can be used in a standard, completely integrated way inside the unification mechanism of the Bousi~Prolog system, what allows us to handle linguistic labels on an equal basis with regard other syntactic symbols occurring in the source program. This is a novel approach because it is the first time that fuzzy sets are introduced into the core of a Prolog system by means of compilation techniques and combining fuzzy relations with weak unification. An important feature of this approach is its simplicity, since the inclusion is carried out in a very natural way without affecting the operational semantics of the Bousi~Prolog language and with very few syntactical modifications. All these reasons convert our approach in a good alternative to the techniques used by other fuzzy Prolog systems.