Annotated Fuzzy Logic Programs
Several fuzzy logic programming systems that deal with fuzzy sets as data in programs have been developed, but they lack the fundamentals of a theorem prover, whence the soundness and the completeness cannot be proved. Annotated logic programs have been developed as an extension of classical logic programs, and proved to be an essential formalism for lattice-based reasoning. It appears to be a suitable framework, but is still not sufficient for development, from the point of view of a theorem prover, of fuzzy logic programs computing with fuzzy sets. This paper proposes annotated fuzzy logic programs (AFLPs) as a formal logical basis for fuzzy logic programming systems involving fuzzy sets as soft data, i.e., data pervaded with uncertainty. The syntax of AFLPs is introduced and their declarative semantics is studied. The AFLP SLD-style proof procedure is then defined and proved to be sound and complete with respect to the declarative semantics of AFLPs.