Optimizing Fuzzy Logic Programs by Unfolding, Aggregation and Folding

Multi-adjoint logic programming represents a very recent, extremely flexible attempt for introducing fuzzy logic into logic programming. Inspired by our previous experiences in the field of (declarative) program transformation, in this paper we propose the development of a fold/unfold based transformation system for optimizing such kind of fuzzy logic programs. The starting point is a set of unfolding-based transformations together with a reversible kind of fuzzy folding, that we have designed in the past. The present work substantially improves this last transformation operation by allowing the possibility of using rules belonging to different programs in a transformation sequence when performing a folding step, which is crucial to obtain better, recursive and elegant definitions of fuzzy predicates. In contrast with other declarative paradigms, in the fuzzy setting it is mandatory to pack sets of fuzzy predicates in tuples, if we really want the folding operation to proceed. This implies the need for re-defining the classical “definition introduction” transformation rule and introducing a completely new operation, that we call “aggregation”, which is especially tailored for the new framework. Finally, we illustrate how the effects of appropriately applying our set of transformation rules (definition introduction, aggregation, folding, unfolding and facting) to a given program, are able to improve the execution of goals against transformed programs.