Approximate reasoning by similarity-based SLD resolution

In (Gerla and Sessa, Fuzzy Logic and Soft Computing, Kluwer, Nor-well, 1999, pp. 19-31) a methodology that allows to manage uncertain and imprecise information in the frame of the declarative paradigm of Logic Programming has been proposed. With this aim, a Similarity relation R between function and predicate symbols in the language of a logic program is considered. Approximate inferences are then possible since similarity relation allows us to manage alternative instances of entities that can be considered "equal" with a given degree. The declarative semantics of the proposed transformation technique of logic programs is analyzed. The notion of fuzzy least Herbrand model is also introduced. In this paper the corresponding operational semantics is provided by introducing a modified version of SLD resolution. This top-down refutation procedure overcomes failure situations in the unification process by using the similarity, relation. A generalized notion of most general unifier provides a numeric value which gives a measure of the exploited approximation. In this way, the SLID resolution is enhanced since it is possible both to handle uncertain or imprecise information, and to compute approximate answer substitutions, with an associated approximation-degee, when failures of the exact inference process occur. It can lead to the implementation of a more general PROLOG interpreter, without detracting from the elegance of the language. (C) 2002 Elsevier Science B.V. All rights reserved.