Fuzzy Order-Sorted Logic Programming in Conceptual Graphs with a Sound and Complete Proof Procedure
This paper presents fuzzy conceptual graph programs (FCGPs) as a
fuzzy order-sorted logic programming system based on the structure of conceptual graphs and the approximate reasoning methodology of fuzzy logic. On one
hand, it refines and completes a currently developed 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 wide-sense 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.