This paper presents fuzzy conceptual graph programs (FCGPs) as a fuzzy order-sorted logic programming sysetem based on the structure of conceptual graphs and teh approximate reasoning methodology of fuzzy logic. On one hand, it refines and completes a currently develped FCGP system that extends CGPs to deal with the pervasive vagueness and imprecision reflected in natural languages of the real world. On the other hand, it overcomes the previous widesense fuzzy logic programming systems to deal with uncertainty about types of objects, FCGs are reformulated with the introduction of fuzzy concept and relation types. The syntax of FCGPs based on the new formulation of FCGs and their general declarative semantics based on the notion of ideal FCGs are defined. Then, an SLD-style proof procedure for FCGPs is developed and proved to be sound and complete with respect to their declarative semantics. The procedure selects reductants rather than clauses of an FCGP in resolution steps and involves lattice-based constraint solving, which supports more expressive queries than the previous FCGP proof procedure did. The results could also be applied to CGPs as special FCGPs and useful for extensions adding to CGs lattice-based annotations to enhance their knowledge representation and reasoning power.
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