Rules

In this chapter, we present a strict generalization of basic conceptual graphs (and nested conceptual graphs). A rule expresses knowledge such as: “If H is present then C can be added,” where H and C are two graphs with a correspondence between some of their concept nodes. H is called the hypothesis of the rule, and C its conclusion. A rule frequently represents implicit or general knowledge, which can be applied to particular entities, thus making it explicit on these entities. The following is a typical use. Let F be a basic graph representing facts and let R be a rule representing general knowledge. F can be enriched by applying R: Each time the hypothesis of R can be mapped to F (F contains a specialization of the rule hypothesis), then its conclusion can be added to F according to the mapping.

In the first section, we give definitions and logical semantics of the kind of rules that are studied in this chapter. The second section is devoted to rule application in forward chaining. After defining a derivation mechanism, it is proven that this rule derivation mechanism is sound and complete with respect to the logical semantics. The third section is devoted to rule application in backward chaining. Backward mechanism is similar to Prolog resolution. But, since a graph rule is more general than a definite clause, the situation is more complex than with Prolog. The graph structure is used in the backward mechanism proposed. The fourth section deals with computational complexity results. It is stated that the deduction problem is non-decidable (i.e., it is only semi-decidable) and decidable cases are exhibited.