Annotated Fuzzy Logic Programs for Soft Computing
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 quantitative reasoning. This 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.